Need help with chuck design

I'm thinking of making a collet-like chuck. It would be collet-like in that it would have a fixed size and have fingers that close to hold. Unlike a collet, it would taper to the front and have a threaded tapered sleeve over the nose:

There are two versions shown, one with a 2 degree taper and one with 5 degree. I can't decide which is better using my standard TLAR (That Looks About Right) methodology. The lesser taper has more mechanical advantage, but requires more turns of the sleeve. Similarly, a fine thread pitch has more mechanical advantage, but requires more turns.

Using the goals of .004 change in the bore with 1/2 turn of sleeve, I can use 2 degree taper and 9 tpi or 5 degree and 12 tpi. The 2 & 5 degree alternatives were just picked out of the air using TLAR. The pitches resulted from the 1/2 turn for .004 close goal.

The biggest uncertainty is which, if either, will provide adequate grip for reasonable torque on the sleeve. The application is to hold a buff or wire wheel, so the needed grip is not that great.

I've got the feeling that this is the kind of thing that I could make a lot of versions of if the approach was to just try something (i.e., TLAR). I think that I need a more analytical approach, but I don't know what it is.

As always, your expert advice is greatly appreciated, Bob

BTW - the drawing was done with DeltaCad. Anyone know how to add cross hatching? Also, to get the jpeg, I PrtScn'ed the DeltaCad window, pasted it in Adobe Photodeluxe, cropped it and saved to jpeg. Any better way?