I've started a transaction of 0,05 BTC (not a huge amount) with the possible lowest (and slowest) low-prio fee, and I thought that it will take days to get confirmed (or at least one day). The fee was about 0,0034... BTC (159 sat/byte).
In an hour (or less), it was confirmed, the first 4 confirmation was done in 15 minutes. I was totally surprised. I've checked the mempool later on, it has been settled, it seems. These are the first few weeks since the beginning of May when the mempool isn't full.
I don't know what has happened, but it seems promising. (Or not, if it's in connection with the August 1st deadline, but who knows... I don't, but if anybody knows, please help me to understand what is going on behing the scenes...)
You probably have the wrong idea, for bitcoin, the charge of each transaction is not the decisive factor for its speed. Transaction costs only contribute to the priority of your transaction. The new priority determines the speed of each transaction.