It's great to be sharing experiences with you all! I decided to open all my packs and set them out to offgas for a few weeks, and I have some encouraging news! The stickiness is markedly lessened over the past weeks, even more than the smell has. The other day I took a few of the stickiest pieces (stairs with engraved tread, like inverse diamond tread, and brown and sticky all over the top) and sprayed it with trusty Dupli-Color primer. And what stickiness was left is gone on the sprayed side. I'm encouraged enough to do up a kit now and spray it, and check the results.
It was bugging that nothing seemed a satisfactory answer. So I've popped off and done a little reading up rather than contemplate the issue.
The most logical and probably answer is hygiene,or the lack of good house keeping. As it appears its possible to get a degree of transfer of debris from the laser base plate back onto the mdf. Which would explain the random nature of the problem. Because in order to get a full frame sticky would require a considerable build up of debris.
So its seems likely we're getting the crappie piece before someone notices the cutter needs cleaning.
Here's a screen shot from a company which Brierley mentions the issue . There's a load of marketing blurb that goes on to explain how they minimize and or avoid the issue.
Good stuff, thanks for sharing! In my case there was even more stickiness on the top, so that should be factored in with this info. For example the inverse diamond tread doesn't cut all the way to the back, and the top is sticky all over, but the bottom just at the edges, altough I think there may be some "splotchiness" tot he back side stickiness in places, where the top is more universe (I see to remember this but haven't gone over to fact-check this statement).
I am also wondering whether shipping could be playing a role here. Though it's winter all the way from Poland to here in California, there might still be opportunities for fluctuations in temperature, and maybe even strong heat.
I would definitely say that some mdf kits have been very soft and flexible and some have been very rigid with beautiful sharp edges. The source/type of mdf could be the root cause.
Hmm... can you out the soft kit manufacturers? The Multiverse MDF is of the hard, crisp variety, and I was pleased with how good the cut edge on the piece I primed was without any sanding first, and how nicely defined the inverse tread.
Plan to come back with a further report with pics. Don't wait up on me, though, as I have other big projects I'm trying to focus on and am actively trying to cut down on my habit of sneaking in a side project like a laser-cut kit in almost behind my own back.

So could be weeks or months or...