You Can't Nerf and Respect at the Same Time
How can I best keep the fights interesting while respecting their character creation choices?
Essentially, you cannot. You're asking for, in essence, "What is my next step in the arms race?"
If you have a party of the expected level and number of players, you don't need any rebalancing to accomplish interesting.
Attempting to ratchet the difficulty up is inherently not respecting their build choice
Increasing the Attack Bonus
This is the most obvious disrespect of the choices they've made. It's an outright negation of their choice.
Modify the Encounters
This is more of the same - tho less egregious. But it's the same problem - you want to take away the advantage they paid for in feats.
Disallow Moderately Armored
This also is disrespecting their choice. You seem to have already figured this out.
Interesting ≠ More Difficult
An interesting fight isn't of need more difficult. It's often non-combat stuff that makes it memorable.
So What To Do?
Use what's there better. Assuming you're running a party of the correct levels (IIRC, it starts at 3rd for the non-encounters version), and have only 4 players, the encounters are balanced. So it's time to use what you've got.
And what you've got are a bunch of nutjob cultists. Have them making brash assertions of skill. Have them use group tactics and the 3rd dimension well. Make use of the terrain. Use the multitude of "save or suck it" spells (like the create bonfire cantrip).
And above all, describe, describe, describe. Don't say, "Cultist 1 attacks Player 2." Do say, "The tall cultist is attempting to impale Fredo upon his spear." Things will get a lot more interesting and memorable just by describing better.
Mechanical Stuff to use
There are a number of mechanical options that can increase the risks to PC's without disrespect...
Give monsters their death saves. This really does make for some tense moments.
Remember to use cover and consider using flanking(DMG optional rule, p. 251). If the ranged attacker (spellcaster especially) doesn't have line of sight to all 4 corners of the target's square, the target has +2 AC (partial cover). If only one corner can be seen, it's +5 AC (3/4 cover).
Use the Lingering Injuries option(DMG, p. 272). Makes crits much nastier.
Grappling doesn't care about weight, only size matters.
The grappling rules do not distinguish from grappling a 300lb Medium-sized creature from a 100lb medium creature. If you're grappling a medium-sized princess, it doesn't matter how heavy she is, your speed is always halved, unless the creature is two or more sizes smaller than you.
So, in your example, the Barbarian could only move 25 feet then dash for another 25 feet. And, yes, they can do 5d6 damage, if everything lines up for them. On subsequent rounds, the Barbarian could just move back down, grapple again and dash up 25 feet. Equating to 2d6 damage on subsequent rounds, not that impressive any more.
It should also be noted that carrying/lifting/dragging an object is governed by different rules from carrying (i.e. grappling) a conscious kicking screaming princess.
Best Answer
Adding on to what has been said already:
You might be able to simply jump up, using a box, table, or cart like a ramp, grabbing your opponent's feet and initiating a grapple maneuver of some kind.
It's possible (depending on GM ruling and the Warlock's behavior) that they will have to stand on the floor or get near you for an attack. This could also open them up for a grapple action or sword strike.
While you said you didn't see your character getting a sidearm anytime soon, if you get a chance to prepare for the fight it's not unreasonable to get one anyway, as your character seems to be aware of the Warlock's ability to fly. (I read your question this way, I hope my assumption is correct)
If nothing else works you can try to throw things at them, be it your sword, a chair, a spear used as wall decoration, or whatever else is near you. If you hit them there's a chance of their concentration being broken and they might fall to the ground.
Source: DnD 5e basic rules page 79/80: http://dnd.wizards.com/articles/features/basicrules
Ultimately you can (hopefully) trust your GM to not throw you into unresolvable situations as long as you don't do anything silly. If you can't run away or defeat your enemy, then there's the possibility of a plot line where you get defeated - but not killed - and saved, so next time you will be prepared for this strong opponent, either in the form of a crossbow or something else.