I'm looking to purchase a pump-style soap dispenser that goes into the
little round port next to the main spigot on a kitchen sink - the
round port meant for soap dispensers, and spray gun attachments.
 Can someone point me to a source for such a thing?

These are generally used in bathrooms, not kitchens, but the second
item down should work fine:
http://www.keysan.com/ksuha46.htm

If you search for "lavatory mounted soap dispenser" you can find quite
a few more choices:
://www.google.com/search?q=lavatory%20mounted%20soap%20dispenser

I'm looking for a less expensive unit meant for the home that
dispenses soap in a foam.