I've looked at doing this a few times. I don't have references handy but there are cheaper atomic oscillators available now, under $1000. Still to expensive for me to justify it but one of these years I'll find one cheap.

A signal distribution box used from eBay is a lot cheaper than a good outdoor GPS antenna!

Though if you have enough cable and enough antennas already, no harm in having a little array like in OP.

I've been testing it and it is noticeably better, but I haven't yet had time to set up an A/B test to get real numbers.

Too bad you couldn't hack the Americium module from a smoke detector and create a DIY atomic oscillator. Cesium seems to be preferred. (And I know nothing about this sort of thing.)

(EDIT: chatting with an LLM… I realize I had assumed that "atomic clocks" meant radioactive and so suggested Americium because it is easy to obtain. LLM schooled me and suggested "Rubidium oscillator modules" instead since they come up for a few hundred dollars or so on eBay. Still not the DIY approach I had hoped for—I think I am still channelling the old "Amateur Scientist" column from Scientific American from the day.)