So if waiting for it to drop off the network may not work as someone else may keep rebroadcasting the TX, what can I do to get this TX through? I have heard I could possibly rebroadcast it with a higher fee, but my wallets won't let me because it considers the funds spent already.
You can only rebroadcast with a higher fee (Replace by Fee aka RBF) if the transaction was marked as "replaceable"... I don't think Mycelium supports RBF and I don't think it marks transactions as replaceable
Even if you imported your private key into another wallet, you would still not be able to do an RBF... you'd have to just attempt a good ol' fashioned double spend... but generally, most nodes will reject your new transaction as a double spend unless it is specifically an RBF attempt