As said 14 days is the time period when most nodes will drop your TX from mempool and its already 1 week since the TX broadcasted now you may have to wait for one more week to see the transaction disappear from your exchange wallet.

So the user has to send the amount back to you with a higher fee if you don't want to get into the same situation.

Paying a miner for $350 worth of TX is most likely not possible, it can be done but you need to find a miner to do that which is unlikely possible in 2023 even in bitcointalk.

I am not sure this transacted amount is for a payment or something but as others said don't accept this as payment until you see at least one confirmation.