I wouldn't bother with trying to fix it. It's tough to get an adhesive to stick to those synthetic stocks. You can pick up a take off stock on eBay for $30-40, or you could upgrade to a Boyd's laminate. That's a kind offer from Madman, but the Axis uses a different stock than the Savage 10/110 configurations due to the Axis' recoil lug being in the stock rather than on the barreled action.
Hog hunter stock won't fit an Axis. The Axis is not a 110 based platform. The Axis factory stock is notoriously flimsy in the wrist with a lot of flex.
A laminate from Boyds is probably going to be your best option and a nice upgrade. Quite possibly and most likely it will even help accuracy. I think they typically start about $150. Here's a link