The hone sounds like a workable solution with sections of hacksaw blades as cutters. Go slow and vacuum/blow out cuttings regularly. Having a bit hang up with a high torque low rpm drill is hard on the wrist. Hope it works out OK; if not the water will be there for another day.
Alright, so following this advice, I fashioned myself a tool from a car cylinder hone and 3 pieces of hacksaw blade. Really messy, but the best I could do with the few metalworking tools that I have.
Tried it out on a scrap piece of pipe - it does work, but VERY slowly. I'd say it takes around 10 minutes to take off 0.5mm from a single section of the pipe. And like Gonzo said, it does not seem to cut cylindrically, more like an ellipse. I am not sure if it is just repeating the existing ellipse of the tube (like I said, it is not perfectly round to begin with), or making it worse. In any case, I guess this is kind of workable, but will take ages. Also there doesn't seem to be any way to make a depth stop for it so that it doesn't damage the bottom of the pipe.
Those spring hones will not cut a cylindrical hole. It will be uneven. A boring bar of some kind in the only way to do that. Also, pvc is a soft material that will clog any honing stone; they are at most 80 grit. A hole saw will bore that in maybe half an hour. You don't need any giant drill. A regular cordless will work. If the hole saws available are the ones with small teeth for metal, you can keep them from clogging by grinding three or four relief grooves on the cutting edge.
This is actually a sound advice - cutting some of the teeth off a hole saw. It makes sense, by removing the teeth I can fine-tune how much it cuts, reducing the torque requirements. I will get a 83 mm teethed hole saw tomorrow and try again. Pity I didn't buy it today - I told my sad story to the hardware store advisor, and he said that hole saw will absolutely not cut concentrically, but will wander off mid-pipe and cut through the wall. Now that I think about it, it seems to me that perhaps he was talking out of his hat... Hole saw should definitely be self-centering, assuming I can start the cut properly.