It is better to create a separate signed transaction to move funds from stuck address to your target new address AND bitcoin address of the "tx pusher". In case of success you will have your funds on your new address, and the "tx pusher" will receive his bounty to his bitcoin address (as both outputs will be in the same transaction).
That's a bad idea. It's likely these funds will be stuck for many more years, and each signed transaction will remain equally valid. Once a signed transaction is out there, it can't be invalidated until OP manages to move his funds.
Besides, it will mean trying to double spend on top of the current problem.