Bass leaves after amp warms up?

"I just got off the phone with Musical Fidelity..
I was assured the M6i is more than capable of handling PSB Synchrony one speakers."

This is a subjective statement. Most listeners out there might be more than satisfied. There is no reason for MF to say otherwise. But there are doubts based on published specs and bench measurements that should matter to a very discriminating listener, which OP appears to be. So there is a CLEAR red flag worth consideration.

I've heard the PSBs sound very good off 100w/ch Rowland Class D switching amp. That would be a good place to start as a reference. I truly believe a good modern Class D amp with good power supply that can mostly double down to 4 ohms can solve OPs problem in a relatively inexpensive and very compact package.

Rowland 100 w amp for reference.

I would ask suggestions for more efficient integrated amp to drive PSB speakers..

There are many well received integrateds out there these days that use CLass D amplifiers, even inexpensive Japanese ones from companies like Onkyo. Quality of power supply, which matters might vary widely with an integrated more so than separates. If the specs indicate mostly doubling down to 4 ohm, it is probably worth consideration. There are still limitations with amp and pre-amp in close proximity in same box with Class D, but technical aspects relating to noise and shielding are different. I have not used Class D integrateds so cannot vouch, but many have received good reviews and acceptance. To be safe, I'd say separates are better (and with Class D amps smaller as well). But why not try a well reviewed integrated for reasonable cost first and see? If it does not work out then move on eot separates. I think there is a decent chance the right integrated could work for OP.