Thanks for sharing!
I have no idea what you mean about the thief not being able to get away clean. Isn't one of the choices that the thief isn't detected in the process? One of my players used this as the very first roll in our game. He nailed it with a 10+ and I think he was able to pick 3 options, one of which was the "no one detects you doing it" option.
The big battle in our game was an absolute blast. It consisted of three PCs, one NPC, and 5 or 6 goblins. I didn't find that there was any trouble coordinating things at all. There were usually one or two enemies attacking an individual target, but I would have gone to the rules for mob/group damage if there were any more than that and would have used some of the usual ways of making things clearer, such as using dice to indicate everyone's position, making some of the individual monsters appear distinct by giving them special equipment or characteristics, and the like.
As a worst case scenario you could probably treat each side as their own unit and handle the battle that way, though I would have probably just kept track on paper and described some nasty group attacks, such as one of the NPCs smashing a frog dude in the gut, causing it to double over as the wind was knocked out of it, giving the PC a chance to come in for the kill.
I found the moves during battle to be my easiest moves (as GM) to make. Generally the players were eager to make moves, so I got to just jump in when they failed a roll with a hard move, or on a successful roll they would narrate their move and I would provide a follow-up or say "what is so-and-so doing while this happens?" I found combat to be an absolute pleasure and seemed to run itself.
I wouldn't worry too much about your PC that's rocking the plate armor. My wife's paladin is doing the same thing. I figure that there will be plenty of chances in the future for big bad monsters to kick her ass. I might propose that you inflict other trouble on that PC when they fail a roll, using a move like "take away their stuff". A player without a weapon is going to have to scrounge and improvise and get involved and won't be thinking they're invincible since they'll be focusing on the trouble at hand.
As an aside to that, my wife failed her Perilous Journey roll and decided to get separated from the party. She wanted to climb a tree in plate armor, so when she had a partial success I described how she got all banged up falling out of the tree with her armor being all dinged and damaged. I'm going to press that in the next session.
I would suggest you don't worry too much about the plate armor and lack of damage because, in my mind, this isn't D&D. It's not all about HP and damage. There are plenty of things that can happen to that character, such as starvation, getting lost, falling, personal trouble, false accusations, magical attacks, loss of equipment, poison, hirelings turning on them, and the like. Poke 'em where they're tender :)
I would "directly provide challenge" like you mentioned. Give them trouble, badness, and challenge. I feel that DW is very strong in that regard because I feel like the AW/DW rules give me explicit permission and lots of techniques for creating drama, challenge, and difficulty. Player moves and rolls naturally set you up to throw difficulty and drama at the players. Look out for those failed player rolls and put their NPC friends, their security, and their chance of completing their mission directly in the crosshairs.
I feel bad for your poor frog people!