I don't know of anywhere the GMRS rules say base stations are allowed only simplex. Although uncommon, it is possible to have separate TX and RX frequencies even when not using a repeater. The issue with base stations is they aren't listed as one of the types that are allowed to use the 467 MHz main channels. It comes down to whether that omission is a prohibition. I would expect a clear statement like, "Base stations are not permitted to transmit on these frequencies." But you never know how things can be interpreted.
And what makes a station a control station is it is controlling something, typically a repeater's functions. Since I don't have a repeater, control stations are not an issue for me. And that lame circular definition that says fixed stations talk to other fixed stations does not tell us what makes one a fixed station. But I've mostly come to the conclusion, even though I don't know what it is exactly, that it won't apply to my use.