A 3 or 4" hole... hmmm that's a pretty big hole to cut with a flycutter on a small machine. The best that I've managed are 1 1/4" holes x 1 1/2" deep using a boring head on my old chinese mini mill.

This was at the lowest speed setting and it still cause a bit of squeeling and low frequency rumple (not good because I was living in an hi-rise apartment at the time)

The problem is that a 3" hole has a circumference of almost 9 1/2" and at only 100 rpm spindle speed you end up with the cutting tool travelling at over 78 feet per minute.

This means that you have to take very light cuts because the cutting tool is held so far away from its rigid support.

Of course a cnc'd hole is relatively easy if you don't have too much backlash in your setup.

Good luck.