An unrelated idea - was have Han call out to Kylo Ren whilst he carries off Rey. I thought this might start Kylo Ren’s doubt and fretting as oppose to reveal it rather flatly with Snoke.
While this has pros, which you’ve listed in terms of it improving the Snoke conversation, it also has cons. I like the fact Han is slightly uneasy about calling his name, even with the relative safety of a retreating first order and arriving resistance force. It adds even more weight when he decided to call out to Kylo later when Han’s much more vulnerable.
Just my opinion…