I think its important to separate concept of rhythm vs recoil, although they are related.
Recoil per se if not controlled causes flip and excess dot movement.
Rhythm is how the gun feels and manifested by dot movement patterns, such as dot dipping or other instability, and speed of dot recovery to zero.
Rhythm is controlled by the interaction of the shooter and the gun. The usual suspects in bad rhythm, exemplified by dot dip, are mismatch of powder to gun (as in excess gas or powder that burns too slowly), comps, slide too heavy or spring too heavy, or bad grip.
Flip can be mitigated by some of same factors as rhythm, but getting back to OP’s question, what can you do besides powder to reduce flip? Two easiest things are to increase grip strength and recoil management with a thumbrest. In my experience, the thumb rest works the best. That will decrease flip dramatically to virtually no movement.
A properly tuned gun will not have dot leave center of scope and will be perfectly up and down which IMHO is best achieved with thumbrest.
And BTW 3 port comps work fine, I have tried many and settled on simple 3 port comp and dot hardly moves. Some great shooters like Jerry Barnhart and Chris Tilley have had excellent results with only 3 ports.