(This forum limits pics, so here is the other part of my reply here)
I have two detailed shots of the "bad" splice, and here they are:
I struggled to get the cover tight over the core in the eye portion in all my splices, but felt like I did pretty well--it isn't quite as "hard" as the rope is undisturbed, but I can only work a tiny bit of slop around...I would guess that pulling 1/8"~1/4" of core into that portion would get rid of it, if that makes sense.
Following NE Ropes directions, after pulling the core out at the middle mark, I loosened the cover all the way up to my knot (doubled figure-eight leaving a loop easy to drop over a winch drum, etc.) and milked it back down before I marked the two points on the core.
I was surprised at how much "extra" core I had out after that process was done, but I figure if nothing was going to change, they wouldn't have included that step.
So...I'm still looking for suggestions on how to do my next set of splices with 100% strength, and also what I can do about trying to salvage what I've done, given that I can live with 50% strength if I trust it that way.
Also, I do intend to do throat whippings on all of my splices, I'm just waiting until I'm done splicing to get onto it.