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 no broadcast transactions. Nodes broadcast transactions to other nodes, while miners use the data from their node to generate a block to attempt to mine.