Just shoot with lenses that have stabilizers built in. Problem solved.
One of the advantages of going to mirrorless with the G85 and GX8 is five axis ibis. Thankfully, as I've gotten older and more shaky, technology has come to the rescue! If I'm paying attention, I can get a fair hit rate hand-held at 1 second with the G85.
I don't think mirror slap is a real issue with the f4, f5 or f6, though. When I used the F4s professionally, though, carrying that boat anchor around for very long could certainly make me shaky!