You mentioned early on that the battery was as far back as possible. There are more possibilities.
If the servos are where they usually are, then moving the pack behind them actually puts the batteries back where they will do some good. If the pack wasn't already behind the servos then it was very probably contributing to the problem.

It's actually not hard at all to place a battery pack inside the fuselage behind where the Trailing Edge of the wing is secured. Get some scrap wood and build a box that fits the pack. Build it around the pack while it's outside the fuselage. It's lots easier to build on the bench. Don't worry about the weight of the wood. After all, you need weight. The box should be open ended, just one opening, toward the front. Fit it into the fuselage back there with something like Elmers or 30min Epoxy.

BTW, try this test.
Remove the battery and check the airplane's balance. Find out where it balances, don't worry about noseheavy or anything. Just find out how far back from the LE at the wingroot the balance point is. Where is it?
Now, tape the battery behind the servos and find out where the balance point is. Masking tape works good. Outside the airplane works too. Where is that?
Now, tape the battery farther back, say just behind the TE of the wing. Where is the balance point now?