I can relate to your desire for casual....
An off white linen shirt would work with the IoS, be light weight and cool in the tropical climate. (Would also help to reflect some of the sun).
The tattersall shirts are an option, but the cloth seems a bit heavy in the Florida heat and humidity, probably similar in your locale... a light shade of green may go as well. Best thing would be to take a friend that is good with color choices and wear your kilt to the shops. Once you have the colors chosen, you can expand your search online.
I find the T shirts to be hot and clingy in the heat of the day.
USA KILTS casual? Great in the hot and humid weather... neighbor found one for me in a thrift shop for $25 with a jacobite shirt.

Might try Etsy as well in your searches...

Best of luck