Okay, here's what I'm doing...
a$ = str(timer())
b$ = ""
for x = 1 to len(a$)
if mid(a$, x, 1) = "."
b$ = right(a$, len(a$)-x)
endif
next x
b = val(b$)
SetRandomSeed(b)
I use this once at the beginning of the program, then again when the player makes a valid move in the game. Valid moves don't occur too quickly, so I'm not calling timer() very often. By just using the decimal part of the timer value, I get a seed that cycles very quickly, instead of one that is tied to how long the game has been running.
It's working well so far.