Fred,
I'm looking at the last picture and have a suggestion or two.
1) Will is right when he says to indicate the part in......do it. Always do it.
2) Reverse the direction of your cut. The deepest cut should be as close to the collet as possible.
3) Spray mist coolant will take care of any heat build up, as well as blow excess chips away from the end mill, which leaves a nicer finish.
4) What ever collet size your using, your part must be the same size. WHAT?
Let me explain #4. If you have Spring collets, like the one in my picture, you've got nothing to worry about. If your collets are similar to a 5C collet then the size of your part should not vary by more than .001-.002 thousands. 5c collets do not tollerate large variations in finished diameters. If your part is too big or too small by .005-.007 thousands, it will still fit in the collet, but the collet will not clamp evenly on each end of your diameter. Too big, and the part will want to push out. Too small, the part has a tendency to wobble.
Back to my picture
This is an ER16 collet. You see how they are split from each end, and they have a double taper. This collet will expand or contract over a .040 range, which allows a .375 collet to clamp a .355 dia. just as good as a .395 dia.
These are well known for their accuracy and tight grip. If you have the budget, consider buying a set of these. Well worth the money.
I hope this helps.....
and keep at it !