6-32 is one of those 'weak' tap sizes. I'd probably step tap the hole.
JFK (just for kicks) drill a hole and tap it with the type of tap you were using. Start it perpendicularly. Get a feel for how the tap begins to bind up after a few turns, even with the best oil on it.
Then try a spiral flute tap (blind hole) or a spiral point tap (through hole) with the hand tap and lube that will be used. You should be able to detect quite readily how many turns it is safe to go in one cycle.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)