Four transfer switches do not seem sufficient to control numerous appliances through 120v panel breakers
NO, you can't do that. That would cross connect circuits which could lead to overloading the neutrals.  While you haven't said, I think the type of transfer switch you have is something like the pic below.
We hate to say it here, but those aren't all that great. They are expensive and limited in capacity. Many here prefer a power inlet for the generator, wired to a breaker with a mechanical interlock with your main breaker on your main panel. The obviously vary by panel but you can get a rough idea from the 2nd pic.  Taking this approach allows you to pick and choose which circuits to run off the generator by turning off or on various breakers.   It's code legal and safe, convenient and not expensive.
EDIT: Thinking about this for a few more minutes, your idea is a really terrible one. You'd have cross connected circuits and the end result is to do any kind of maintenance you'd have to turn off multiple breakers to depower a circuit. PLEASE don't do this. Others have commented just now saying a mechanical interlock is best and ironically, least expensive.  As 3ph said, please shoot us a pic of your main panel to better help you.