When drilling SS centerposts, one must needs go with very slow RPM. My drill press only goes down to 700rpm; but I make do. Also, starting with a brand new, sharp drill bit is a must. Cutting fluid (say, Rapid Tap) is ding-dang helpful too . . . .. it could make or break your project, so let's say it's a must. It's not a question of power, some folks do this by hand (i.e. spinning the drill bit by hand); more likely, it's a question of your drill bit going dull and/or "work hardening" the steel. As soon as one bit begins to lose effectiveness, one must stop and change bits. If not, you're just spinning the dull bit and work hardening your steel. If you're not cutting deeper, you're rubbing/heating/hardening.
Is the Trident centerpost mounted in the standard fashion? If so, you could swap for another centerpost. Many of them seem to be of the same shape and size (on the fitting end of the deal).