Hello again, and you're most welcome. Thanks very much for your accept and most generous bonus.
I'm glad you found the cause of Jilly's itching/scabs! I didn't realize she goes outside to sit in the sun. You said she was an indoor-only kitty, so I thought she sat in the sun in a windowsill, etc., inside. Something else occurred to me, in re-reading your original post. You said she seems to crave warmth all the time.......this could be the result of anemia, from the flea feeding on her blood, so check this out at the vet's.
Yes, the remodeling could be stressing her out, so try to keep her as far away from any area being worked on and the loudest noises, in a 'safe' room with a closed door. If Jilly is stressed/anxious, due to the noises of the remodeling, she might benefit from a cat appeasing pheromone called Feliway/Comfort Zone for Cats, which comes in both a spray and plug-in diffuser. It's available at major pet supply stores, and also online. The diffuser resembles a plug-in air freshener, but has no scent to humans. Feliway helps to relax stressed or anxious cats, and is useful in a multitude of situations. For more information, please see: www.catfaeries.com/feliway.html
If she continues to seem to fur-pull after the flea problem is ended, discuss a low dose anti-anxiety medication to help her feel less stressed, with her vet.
You are very wise to replace your carpeting with wood floors, and now that you've started Jilly on Frontline, it would be wise to have your home and yard/garden treated professionally for fleas, to make sure the problem is gone for good. Treat the other cats who go outside, with Frontline (or Frontline Plus, which prevents fleas and ticks), monthly, as well. If you're located in the USA, a company called 'Fleabusters' is excellent; they are exterminators who specialize in flea removal. www.fleabusters.com
I've used them myself, and they are great.
Check out the possibility of anemia for Jilly and I hope she's feeling much more comfortable, very soon. In addition to checking for actual live fleas on her, and your other cats, signs fleas are present are black specks resembling ground black pepper, which are flea 'dirt' (excrement), actually made of digested blood (after all, a flea's 'meal' is blood), so you can check all your kitties' coats/skin for these specks, constantly. Also, combing with a stainless steel flea comb every day will help you see what's in their coat.
Once they are treated with Frontline monthly, and your home/yard are treated, you should see no more problems. It might take a short while to see no fleas at all, but it will happen. I speak from experience (unfortunately!) : )
I wish you and your family much good luck with the remodeling and hope all will be well with Jilly and her siblings.