Please let me know if you have another idea.
Child-Pays-for-Parent will work in your case, you just have to spend that specific output and it'll bump its fee.
The problem is, nodes with default mempool size are now beginning to drop 1sat/vB transactions and yours might have already been evicted from some nodes' mempool.
Can you tell what wallet are your using?
Because depending on which wallet, there may be easier way to perform CPFP.
And depending on the state of mempools, you might have to rebroadcast it or wait for the average mempool size to settle a bit lower.