Plugging and redrilling is really the only option if you want to use the thinner bushings. You need a tight fit, particularly with a wrap-around bridge, otherwise the posts can start to tilt forward under string tension lifting the back of the bridge and causing action, intonation and tuning issues.

But, before you start plugging and redrilling etc. have you checked the string height/action with the new bridge? As you have now glued in the neck its angle is fixed, so if you need to make any adjustments for the action it will have to be done at the bridge. Best to work out exactly what the current state is before you start drilling.