Everything you have listed could be single phase, which means that
each item will cause the reading to go up in only one phase of the
circuit. If you do have 240V stuff it will cause both phases to go up
at the same time.

Yes, all of the equipment is single phase, some on one leg, some on
the
other. This is the source of my dilemma. So what I really am asking
is this: I know its meaningful to measure the current on one leg or
the other, but is it meaningful to measure the current on both at the
same time?

Say I was drawing 8 amps on one leg, and 9 on the other. Am I
using 17 amps? That seems right, but does it have any meaning?

The 30 amp breaker is 30 amps per leg - So who cares if they both
add up to, say, 40?

I'm starting to think measuring each leg independently is the
most correct solution.