1) I did pay for inside wire service from Verizon to start out with, under
the
logic that I want the phone company to fix anything that I find in the
first
couple of months in the new house. Will they generally fix botched
installations
for free under this kind of plan?

Call them and find out. I'd guess 'No' but I've never had an inside wiring
plan.

2) If not, any suggestions for fixing these jacks, preferably without
butchering
the drywall around them (since the painters are there starting today)?

If the holes aren't bigger than a normal junction box opening you should be
able to go to Home Depot and get some plastic junction boxes that have screw
tabs so that after you insert them into the wall and turn the screws some
tabs fly out on behind the dry wall and lock it all securely in place. All
you have to do after that is to fix the connections on the plate and screw
it to the junction box and your done. I recommend unplugging your inside
wiring from the phone service out at your service box outside your house so
that you don't get surprised by a phone call coming in and get a possible
shock.

Brad