I have the Delta mobile base and the wood, so from a cost standpoint, that
seems to be the better option. The only downside of this mobile base is
that it has a pedal that raises the front of the base to make it mobile
and I am concerned it might case the drill press to tip over, though I
think it is relatively unlikely that it would and I won't be moving it
around much.

The Delta mobile base (with decent quality wood runners) is more rigid than
the other metal mobile bases I have. Since you already have it, you might as
well use it. I'd suggest bolting the plywood to the runners, and maybe a
couple of supports underneath the plywood to strengthen the platform, as
3/4" plywood will likely give a bit with all that weight on it. You should
be able to adjust the amount of lift from the foot pedal so that it's no
longer an issue.