There are things you can do make large battle scenes more tolerable in PF/3.5, such as;
- Grouping Attacks - Similar units with similar attacks are grouped into 'volley' attacks that are dodged with either a saving throw, or are fewer attacks that deal more damage.
- Placing Fights - creating larger 'maps' for fights with terrain that separates groups of combatants allows the players to use terrain and selectively engage enemies, turning a 'large fight' into a series of smaller fights.
- Treating Groups of Enemies as a Single Creature. Roughly what the DMGII's 'Mob' template does, treat a group of weaker creatures as a single creature with it's own hp and attacks. HP being whittled away kills members of the group, but it still only has one set of stats (although probably a Swarm attack).
- 'Battle', treating weak enemies as a terrain effect. They're rough terrain and deal environmental damage to the party, but they're not units with hp - by moving through them, the party is killing/fighting through them, but the party's real enemies and real goals in the scene are unrelated to them so they don't roll dice or do more than hinder the party. Like orcs in a LOTR battle, the party spends it's actions shooting down oliphants and stuff, killing orcs happens 'during' their other actions.
- Waves, enemies come as relatively discrete encounters with a time pressure of if you don't wipe them out the next wave is going to arrive. In this case, the papermancer would be origami'ing new monsters as the party cut down the ones he has already made, and doing other things like sending waves of sharp-edged paper birds through the group, sending paper streamers in blue hues to 'flood' the party and ruin their footing etc (you can refluff a lot of spells to be origami).
But you shouldn't be hanging everything on a single battle anyway
Any good villain is foreshadowed. Paper mantis assassin striking the party in the night, learning about the man who wears a white paper mask and kills with paper knives, thugs wearing paper armour with paper swords (that are made from scrolls, and the thugs can activate them), an ally of the party being killed a paper chain that climbs singing into his mouth and chokes him to death at a dinner party, the climactic fight at the hideout alongside their allies, the papermancer boarding a paper dragon to escape, the final confrontation on the mountain where he defends the diggings of the Jade Lotus society's attempt to resurrect a dead god, defeating the papermancer who fights to the very last with no advantages to defend a man who isn't worthy of that loyalty, thereby giving the PCs yet another reason to hate Marcus Stein, aka Xaoyao Luyfu, the Hidden Master of the Cult of the Jade Lotus.
Etc etc. You introduce, you create importance, you cause confrontation, you (hopefully) escalate the confrontation, and then you add twist to season, either twisting to make the character relatable or sympathetic or to make them even more horrifying than the party ever dared suspect.
That's what makes a memorable villain. Large fight scenes can be story-required, like if you foreshadow that the papermancer if given time can create a paper-army, and then the party gives them time, but they do not create memorable villains or highlight interesting story features.
Outsource it to your Players
I find this happens in games where there is an unspoken agreement that the DM is going to in charge of (everything) about the world, and the players are going to be in charge of their characters, and that's it. That is, historically, the way games have worked. But it isn't the only way they can work.
You could for example, sit down with your players, and talk about what kind of game you'd like to play, what kind of challenges they'd like to face, and ask them how they'd like to balance those interests. You can bring up these issues, and ask them for solutions. If nothing else, it'll prepare their minds for there being times in game when they won't get to do their favorite thing.
Build the Game Together
There are tools for building a game. Depends on how deep you want to go. If you're comfortable taking a lot of input from players on how the world is going to be, you could use Sparks For Fate Core. It's built to use with the Fate RPG, but there is absolutely no reason, if you understand Fate as a game, that it can't be used to build worlds for other games. You don't even have to allow Aspects to mechanically influence the game, just use Sparks as a worldbuilding tool.
This will likely make your players more invested in the world, and so they'll be more interested in the roleplaying opportunities you present. The GM still has ultimate say over what happens in the game, but the players get to say what they're interested in. It might depend on your GM style, and whether you're comfortable adapting to player input into the setting. For me, it actually takes work off of me to not have to come up with things I think will be interesting to the players. I can simply riff off of the things they've already told me they're interested in.
Taking one step back from the setting/game design of Sparks, you may find The Same Page Tool useful. This is a series of questions that prompts the players and the GM to talk about their expectations. As mentioned before, a lot of things can be unspoken in games because of a misguided expectation of "building suspense" or "preserving mystery" for the players. I'm here to tell you that you can talk about the meta game, and still have the in-game moments be fun and surprising. Throw out the unspoken rule that the first rule of the game is we don't talk about the game.
Rolemaster is an old school game that had a section called Gamemaster Law, which is useful to anyone who plays RPGs, whether or not they play Rolemaster (I never have). Like the astrological Zodiac, it categorizes players into different types according to their proclivities while playing, so that you as the GM can better organize them and deal with their needs and potential problem areas.
Try to remember that humans don't always fall neatly into stereotypes, but the ability to say "Oh, Kyle is a Dragon, he's gonna wanna loot all the corpses, I should probably prepare for that" is often useful. Or, "Stan is a Hound, he's totally going to want to find out what the barmaid knows about the missing caravan, I should probably give her stuff to say"
This answer assumes you are all OK with all players and the player characters knowing each other's hit points (hp are a game mechanic. The characters can see if someone is bloodied, it is less clear if they would know anything about hp). All of them essentialy redistribute the work to each player broadcasting their hit points, instead of the healer trying to track them.
If you are using Roll20 with pogs on battlemaps, you can connect the character sheets to the pogs to automatically update hit point display if you change the hit points in the character sheet. Or you can just manually populate one of the fields in the pog to display the hitpoints. You can set permissions on pogs to "controlled by all players" so everyone can see/handle them.
We use the green, middle field on top of the pog. If you provide both the current and maximum value, it even can generate a little green bar underneath that shows how much of 100% is still remaining. If all players update their hit points there, there is no need for the healers to track them separately.
Hit point hats
This is a fun way to track them if you are on camera. Everyone wears a hat and sticks a little note card into front of the hatband that displays their current hit points.
Back in second edition, playing at the table we used to do this with a single hat for the player who had the least hits remaining, or "Mr. Hit Point". This gave the DM a subtle hint and allowed them to not accidentially take him out.
Have people call out
If healers tend to heal characters that are down to a certain low number of hit points, you can have the characters just shout out that they are badly hurt and need healing. Speaking is a free action.