Not sure exactly why this problem has been so persistent but my guess is because of the following:
1. I've been using a full wood core tip to tail
2. the tips have been 2 - 4mm thick (too much resistance?)
3. I wasn't using AL sheets for lay up (hard board cracked)
4. FG not wetted out thoroughly (no excuse...)
And probably other causes too. The problem wasn't as bad when I used tip spacers. I did not pre-bend the wood core in my test, although I'm sure that would help too.
Things I did differently in the tests:
1. Pre-bent base/edges to conform to the tip block
2. Wet out FG thoroughly, did not spare epoxy for the tip
3. I'd been doing 3/4 wrap edging and then filling in the gap at the very tip w/ base material. This time I filled it in w/ 1 layer of FG.
4. The test samples were a 2mm core and a 3mm core.
Pressed normally, left test pieces in for 18 hrs. (I don't plan on leaving it in that long in the future, just worked out that way.)
Took the pieces out this morning and they looked much better! I will clean them up over the weekend and post pics.
Here's they are straight from the press:

Edge shot of the 3mm layup. Sorry for the poor quality. Once it's cleaned up I'll post a better pic.

3mm core

2 mm core

Edge fit wasn't the best, no excuse for that. But I think I have the edge fall problem licked.
Thanks for all the feedback and help along the way.