A transaction paying a low feerate is equivalent to signaling low urgency.
Miners select transactions in a way that maximizes the revenue for their block. This results in the queue of unconfirmed transactions generally being processed in order of the feerate of the transactions. Therefore, the way to get quick confirmations is to pay an appropriate feerate.
You may however be able reduce the overall fees paid by using more inputs when sending at lower feerates, and using fewer inputs when sending at higher feerates.
If your question was about how to figure out the lowest feerate to get confirmed in a time-frame, you could perhaps still improve your feerate estimates. Alternatively, you could consider investigating replace-by-fee and implement your sending procedure such that you increase your transaction's feerate automatically over time if the transaction hasn't confirmed yet. To do this in the most thrifty way possible, you'd need to have a live view of the current mempool, though, but you could perhaps just revisit every 15 minutes and increase it by 1Β sat/vB while it's not confirmed yet. If you start at the minRelayTxFeeRate
of 1Β sat/vB, that would get you to 13Β sat/vB in three hours, which should get you confirmed usually in the current mempool weather. Note that frequent RBF'ing has privacy implications.
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