What backing materials do you have at your disposition?
Without precision power tools (?), bamboo backing an existing bow isn't the easiest thing to do. Sinewing isn't too difficult, but getting tendons prepped into sinew fibres is another thing (not my favorite passtime). Sinew will not overpower the belly or cause chrysals/fretting, it's too elastic for that. If you sinew it, keep the bow short (60" or less).
Flax is easy to apply (like sinewing), but it's very strong so keep it thin. There are other plant fiber backings that are very useful too and a bit more elastic.
Rawhide will protect the back, but it will likely make the bow a bit slower due to the extra mass and hardly add any draw weight.