In my humble opinion, just pay a bit of a higher fee to avoid the inconvenience next time.
It's not actually paying a higher bit of fee but choosing the higher fee will be different when it comes to time transaction. Accelerators can be used also with this kind of issue paying with a small amount.
Most of the problems like this happens when the transaction amount is almost same with the transaction fee.The bolded part doesn't make sense. It does not matter if you are sending 1btc with 1btc fee and 10k satoshi with 10k satoshi fee, what important is the fee per KB of your transaction size. you can send thousands of bitcoin in a single transaction and pay only .001btc, your transaction will be confirmed if the size of your transaction is just small