They absolutely talked about automating GS notifications, via a system that could make a bunch of calls simultaneously. Main goal appeared to be freeing up scheds' time; the alleged gain for the pilots would be, in theory, that the "correct" (senior) pilot would get the GS before getting stuck in the 3-hour window.

No discussion that I recall about how that would be implemented. Your scenario is one possibility; another is that you would be provisionally awarded your GS, and only actually keep it if a senior guy called in within 10 minutes. I suspect the best solution would be to automate the response(s), too, and only make awards at the end of 10 minutes. We won't know unless/until they get this done, but it's outside of the contract....