By the way, I'm not using auto-sensing switches, so these Linksys models have an uplink port. I want to make sure I have things set up properly. Am I right in assuming that the switch that is farther away from the router is the one that gets connected to its uplink port? In other words, in my above example lets say that switches #2 and #3 are 8-port switches. I would run a cable from port 1-7 on switch #2 to the uplink port on switch #3, correct? And the 200' run is plugged into the uplink port on switch #2, right?

I was under the impression that this was how it was done. Just to make sure (because I'll try anything at this point), I've reversed it and even not used the uplink port. This either didn't help or just shut down the network entirely, as you might assume