Ok I agree with Pat, but have tried to save some shot in bows with sinew with success, I agree starting a new bow gives higher rate of success,, the one that comes to mind had worm holes and lots of knots,, the sinew backing made it shoot good for many years, so I think its worth a try,,you might just use a scraper and take off all the finish,, I dont know how thick the growth rings are,, but if they are thin go down one more cause the sinew is gonna add quite a bit of weight to the bow,, I would use 4 or 5 layers since the bow has a bad spot and put an extra layer on that spot first, and leave it stiff when you tiller so it dont work so much,
I wouldnt go crazy putting reflex in the bow ,, your main goal is to get it shooting, not be a rocket launcher, I think if you approach it with moderation it will shoot for you,, clean the back good as suggested and scrape grooves in the back with a hacksaw blade,,
make sure you size the back good too,, coat the belly with glue or paint to reduce cracks from the sinew drying,, dont forget to use boiling water to rinse the back after cleaning with soap,, I use lye, but I am neurotic about the back, and I dont touch it either unless I have gloves on,, I feel sure you can get your bow shooting again,,