I appreciate the advice Godra, but I don't see how that will provide me with any information I don't already know. It works when I give every PLC its own dedicated driver and it works when I pass new IP addresses to a single instance of the driver. In my test setup, that has been a total of 3 different PLCs.
I looked for documentation, but the page for EthernetIPSLCMicro is blank. I'm not going to try and decompile Archie's work to see how the driver works under the hood to see if this is a bad practice. I know that it's pretty much a wash as far as programming time goes either way I choose to do it.
Again, I appreciate this community as it has helped me overcome many obstacles when developing with AdvancedHMI and am very thankful for everyone's help, especially Archie's work.