I'll one up your trick, run a form tap down the hole(not my idea, came from a forum). A .187 I do believe is a #10. It will support your dowel the entire way down the hole, not just at the top.
For the record, I only use this in house on fixtures that require press and slips, I only need to find and use one reamer to get the press and the slip. Parts that go out would never ever receive this treatment.