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.
Probably you are right here. I wrote that from the position that all the transactions
are not accepted by the network. However at this moment we have the case that the spending transaction is in blockcypher:
https://live.blockcypher.com/btc/tx/7da3515aa3a7492b9e99ef95b7a3e7bbaf500c474de68b3dc4c756d18729abdd/
However this transaction is not in blockchain.com and others. So, yes, different transactions posted in different places could compete with each other and stuck for much longer period of time.