How can I get my players to engage in the authentic roman atmosphere I've created?
This reminds me of a well known author who said (paraphrased) that if they spend weeks researching it, there'll be a whole chapter on it!
So, slow it down and give them little bits to digest. Let's go with food as an example: a friendly NPC invites the PCs for a dinner party where NPC plans on impressing the local governor. Sadly, a day before the dinner the provisions get stolen/burned/whatever. So, the NPC asks the PCs for help: find me food and chefs to cook/prepare it! By the end of this short adventure, the PCs will know more about Roman food than you expected. Of course, this leads to the temple of X where some priests find that the NPC has "offended the gods" and took to humbling said NPC. This leads in to exploring religious dogma and theology as a follow up.
In addition, you can set up some mysteries that require in-world knowledge to solve. For example, knowing that a legion always travels 20 miles a day is vital in planning where the PCs need to flee from the Barbarian horde wanting to skin them alive. Another example, the guy offering to help the PCs might not take too kindly to be laughed at because he carries a wooden sword. Just make sure that your players know about those facts or can find them.
So in a nut shell: Make it small and relevant to the PCs. The players should then run wild with it.
In addition, I would look at your surroundings: music, lighting, snacks, and so on. What can you do to make this more Roman? You do have olives as snacks, right?
You're right, combat only challenges get pretty boring. So in a long term campaign, it's good to have a bunch of other kinds of things that PCs can spend their time on.
These tend to break down into three different kinds of things.
- Action scenes other than combat
- Non-action skill-driven challenges
- Strategy and Diplomacy
Action Scenes Other Than Combat
I'm running a pirate game and we've had entire sessions that were "man vs nature" scenes where they were trying to keep their ship intact and on course during a storm, for example. Chases, competitions, jousts, sports... Instead of killing the boggard tribe, how about participating in their weird frog sports to win them over? The first RPG I ever owned was Star Frontiers, and in the initial set of modules the PCs crash-land on a planet (Volturnus) and can win over a weird tentacly indigenous alien race, the Ul-Mor, by participating in their version of Buzkashi. Some of these will have similar-to-combat elements, just are more subtle than pure carnage.
Somewhat related are challenges that are still combat, but have a goal other than "kill the other side" - like trying to repair the dam before it floods the village, but there's some agitated bee swarms attacking them. It's a combat, but since the goal isn't the combat per se but to accomplish something (and all the usual options are here - defend a place, take something somewhere, defend a person, or the reverse) then it feels a lot different and can be accomplished in non-straightforward ways by the PCs. Like if a scrag washes up on deck during the storm at sea above; it's not a "CR appropriate encounter" and the goal isn't to fight it, it's more of a combat complication to a non-combat scene (and they'd be happy enough to just push it overboard rather than fight it to the death). Also, just keep in mind that Pathfinder isn't a computer game where all these kinds of challenges have to be separate - you can mix/match/meld them at will (e.g. a duel with a noble where your main goal, besides not dying, is to use the opportunity to lay some charm down on the princess who is attending - a skill challenge amidst a combat).
Non-Action Skill Challenges
Exploration is the most typical example, and there's loads of opportunity for that in Kingmaker. Dungeon exploration is more about obstacles and traps and tricks and puzzles, but outdoor exploration has its own charms as well. Use the weather, make it realistic - getting lost, avoiding encounters, learning about the land. Travel isn't simple without monsters! How do you get your mounts across that crevice? See also What can I do to give the players the same feel their characters would have about wilderness travel? for more on making travel interesting. I like rewarding skill use, so Survival etc. can be used to detect/avoid random encounters, for example. You can make this as crunchy or non-crunchy as you want - there's loads of discussion on this site and others of "old school vs new school" approach to exploration and whether you do it narratively and make them verbally fondle the puzzlebox or whether you just let them roll Disable Device and be done with it. One of the benefits of the former approach is that it gives it more 'screen time' and cuts down on combat's share of your hours.
Strategy and Diplomacy
General planning and creating things is a great challenge for players. In Kingmaker, in fact, the entire kingdom-building part of the system is designed as a huge non-combat type challenge. Can you make a kingdom that makes money? Can it weather the travails of life in the River Kingdoms? Expand on this; if you just use the bare bones provided in the AP then it can be a bit of a flat minigame, but if you have the characters engage in-character with the rounds of building and economics and all, then it is actually the most meaningful challenge of the AP.
Similarly, a lot of Kingmaker can and should be about making friends, enemies, trade partners, etc. Though poor GMs can certainly "turn this into one or two rolls," as @BESW warns, I strongly disagree that this is a necessary path in d20/Pathfinder.
For example, my PCs' pirate crew is always looking for new pirates. Sometimes they impress prisoners, but they also have open calls when they hit a pirate city. They'll spend hours interviewing pirates, checking up on their history, giving them a tryout (sometimes escalating to combat :-)... Sure, I could just have them "roll Diplomacy to see how many recruits you get, they are all indistinguishable level 2 warriors, done" but they really get into the details, so it turns into an hour-long scene instead.
In Kingmaker and other APs you'll find a lot of support for this; they often have whole chapters about choosing who to try to get on your side (often there's some specific quest involved with it, of course...).
But This Is Up To You (and Them)
The AP itself won't have lots of this. Now, it does have hexcrawling and kingdom building rules, but it's easy to treat them as a minigame. They fill page count with big stat blocks and NPC backgrounds. It's up to you to flesh out the actual campaign with the kinds of things your group enjoys.
Best Answer
Here are some ideas for dealing with overly clever players.
Let the wookie win.
Sometimes the party does something clever. You can take it away in a contrived fashion and they'll resent you for it. Or you can give them bragging rights and they'll proudly tell all their friends about the time they took down a dracolich at level 3 with a potion of invisibility, a dozen tooth picks, and a squirrel. Even if it breaks your game session, this is something the players will look back on fondly.
Don't make your challenges winnable.
I used to throw challenges at my players with a solution in mind. Then I realized that there were four through seven players in my games. Even if I was the smartest person at the table, the sum of the things they could come up with was not a strict subset of the things I could come up with. They'll think of things I won't (and if they can't, that's my failure for picking boring players!)
The point is I stopped working out a win button for all my challenges. I'd usually have an approach or two in mind, but I wouldn't chisel away the difficulty to make sure that approach worked. Often my idea was just a starting point and needed one or two other contributions before it could work.
One of the advantages with this approach is that when the player does something clever to beat the challenge, you'll be delighted instead of disappointed.
(Note that I'm not saying make the challenges unwinnable. Just refrain from taming the challenge in order to make your win button work.)
Spy on your players
This is where you take advantage of the fact that the players will come up with things you can't, and exploit them for it.
I ran a thieves guild game a while back. Instead of dungeons we ran heists. I'd give them a goal with some weird premise for them to work their way around.
At first I mapped out everything. This wasn't feasible long term because I didn't know where they'd be approaching from. If I drew out the whole castle I might forgot the sewer for instance. It became obvious that I'd have to improvise.
The thing that was interesting about improvising is that the players really got into planning. They took longer to plan their heists than to run them. While they were planning, they tried to enumerate all the angles of attack and come up with contingencies for every way the target could defend itself. And they did this in front of me.
GMing that game meant taking notes of what they wanted to do and drawing really quickly. I sketched out maps of the paths they could take (usually as they scouted them) and listed the defenses they thought they could overcome, paying particular attention to the ones they thought of and then forgot midway through planning. I added my own ideas too and wasn't just poaching hazards from the players.
Anyway this approach let me use the players' cleverness against them. I was able to use it constantly in the heist format. Not sure if it's something you can do every session elsewhere.