As a percussionist/drummer, I'd be better able to read the part if the cymbal/snare drum (hands) was written all in a single layer with the bass drum (feet) in a separate layer. 

Yes, that's what I'm trying to accomplish. How can I make the snare rhythm fit under the cymbal? 

and somehow share the cymbal beams?

You've already done that for counts 1, 2, & 4. To get count 3 to fit, use 16th notes. Ont the first partial will be cymbal and snare. Second partial would be just snare. Third partial would be just cymbal, and fourth partial would be just snare. I'll work up an example and post back in a bit.

It would look like this when completed.

This is another option. I find this a bit more difficult to read, but that is a personal opinion.

I think I understand now. I like the first option. Thank you very much, Ted!

Glad to help.