One very minor nit...the PDP-7 where Unix started out cost US$72k+ in 1969 dollars. Nothing compared to the big iron of the day, but very far from a microcomputer (and, really, that market didn't exist until 1972 or so).
Maybe not that much, it next moved to the first model of the PDP-11, which had a max of 56 KiB memory of 8 bit bytes. Then to an 11/45, which could do 64 KiB of code, 56 KiB of data and 8 KiB of stack.
No PDP-11 AFAIK have a separate, dedicated stack space. You're thinking of the 8k dedicated I/O page.
However, as I recall (from the very early '80s when I was using both a 11/44 and 11/45), the MMU had a 8 KiB page size, so the natural thing to do was to divide the data as described, so a stack overflow would trigger a trap. Although after a bit of time with Google, I note the 11/40 manual says all PDP-11s have a location in which to put a stack boundary, so maybe that was a convention which matched what the MMU could do.