So it looks like the Nightly build has the new option called "vintage_use_clipboard" by guillermooo.
As far as I can tell, this solves one direction - yanking things from Sublime will go to the system clipboard. Which is awesome!
However it looks like the other direction isn't working, i.e., when trying to paste using "p" in Sublime, even with "vintage_use_clipboard" on, pasting is still done from the internal Sublime yankring. This is inconsistent with vim's handling of this.
Btw, I'm unclear whether it's "vintage_use_clipboard" or "vintage_clipboard = unnamed".