Hi Larry…
I can't give much advice about removing the quill but I had the same problem on a brand new larger drilling machine, there was about 1/4" play in the quill caused by the pinion gear being too far away from the rack, as you say it is really annoying!
I remember I had to take out the return spring and remove the pinion or else the quill will not move down as the rack gearing finishes at the top of the quill.
I thought of stuffing some thin shim material in between the rack & pinion as a quick fix, but I doubt it would have kept in place very long, I also considered making a larger pinion gear to solve the problem but to get an accurate measurement to make a new pinion and actually making it seemed a difficult proposition.
I took it all apart and machined the drill head casting making the pinion shaft bearing hole larger in order to fit an eccentric bush which I then set over to cause the pinion shaft to move closer to the rack and fitted a screw to lock in position. I used a flycutter to machine the larger hole.
The result is that the quill moves with no slack at all and gives the drill a much more sensitive feel about it.
Hope that hasn't put you off having a go, I found the machining of the cast iron was quite easy, cast iron is ok as long as you don't have to go through the tough outer cast layer… hope you do ok with it.
rgds..Bob.