A university probably could get a ride on a MOSIS run
or some other multiproject. Buying a full mask set and
wafer lot is very expensive, even on obsolete foundry
flows and prohibitive on anything cutting-edge. The
packaging and assembly, you can get done cheaply
(relative to foundry costs) at quick-turn assembly
houses; the setup charges at a straight, volume
production would be higher if they wanted your one-off
business at all.
You might want to look at stuff like the fabless
semiconductor industry associations, look at the
MOSIS web site for some rough idea of pricing and
requirements.
If you are doing this all without guidance, you have
an education coming.