Your transaction may take a longer time to be confirmed since your transaction already broadcast and received 1/6 confirmation, but certainly, it won't be cancelled since it has already been broadcast the minner is just waiting for the network to become less congested before the transaction goes through.
You sound confused. Once a transaction has its first confirmation, the fee it pays and how congested the mempool is are both irrelevant. It will gain one more confirmation with each and every block which is found from that point on.
But Op's own situation is different from yours since he uses low fees and that results in no availability of any miner to broadcast the transactions
Miners do not broadcast transactions. Nodes broadcast transactions to other nodes, while miners use the data from their node to generate a block to attempt to mine.
Now that (unfortunately in my opinion) there are ordinals and taproot, what if in 20 years from now the network is congested and the fees are much higher than the transaction I have signed?
I'll link here my response in another thread for anyone else who is interested:
https://bitcointalk.org/index.php?topic=5451060.msg62205489#msg62205489In addition to hosseinimr93's suggestions above, there is also package relay in development which would allow you to use CPFP even when the parent's fee is too low to be accepted to the mempool, and you can sign the timelocked transaction with a specific SIGHASH which would allow the recipient to add an extra input in order to pay a higher fee.
