However, since the transaction has not been confirmed by the mainstream mining pool, I hope to be able to package the transaction directly into the block through independent miners or small miners to ensure that the transaction is confirmed as quickly as possible.
That is NOT how mining works. A tx must first be packaged into the work sent to a miner either from your full node or from the mempool. Only when your miner or one in a pool finds the block
based on work with your tx in it is it confirmed. Until then it is just another tx waiting like all the others and if someone else finds a block using work that does not have your tx in it, your tx will have to be put into new work to try again. and again. and again. and again....
The fastest way is to just get it into the mempool so all miners can see it and if it has a decent fee they will include it in work being processed.