Hey Sean,
I'll jump in on this one just because of 15 plus years as a working, licensed hardwood lumber inspector.
First, the ambient moisture content is lower in the winter than any other time of the year. It sounds wrong, but it's so. Usually between 2 and 4 % lower than in summer.
The reason I point this out is that the material you are using may have been dried, but not Kiln Dried. Especially common with the exotic materials from third world countries you mention. That's why they usually have wax covering it when you receive them. That means that it is always only going to be as dry as the moisture in the air around it. And I don't care if it's been air drying for 100 years. As it takes on moisture...it will swell. as it dries out...it will shrink. UNTIL...it's sealed throughly!
So that's why stabilizing is so good for reclaimed and none commercial natural products like old deer antler or that stump of walnut you dug out of the back yard and cut up to get the root burl.
The kiln drying process mechanically forces the moisture out of wood down to 5-7%. This collapses the cellular structure in wood and stabilizes it by reducing it's ability to absorb moisture without prolonged exposure. Kind of like a raisin. No matter how much moisture you add back to it...it's never going to be a grape again. ;~)
What's probably happening in your case is when you cut out your dimensional pieces, you expose more of a thinner cross section of the wood. It can then leach out more trapped moisture. You work the piece, mount it and the whole time it is shrinking. You bring it in during the winter and the moisture content is down already and the heating system is drying the air even further. As it dries, it continues to shrink further.
The simple fix is...cut your pieces long before you need um. Wax the end grain very well so they don't crack and then let them set for a while. Within a week or two you'll be able to actually measure a couple of hundredths of shrinkage. Then you can shape the pieces, soak um in you're favorite oil for 24 hours (I like natural danish oil) and finish um. Shouldn't shrink much further.
Or you can stick the pieces in a microwave on defrost for a few minutes. If you're crazy enough and have a very understanding wife. LOL
But be careful if you try to nuke um. Besides the stank in the house and risk of catastrophic fire, there is a good chance of cracking the wood if you go to far to fast. None of which are outcomes I want to risk devoice over. LOL
Good luck man. It's a pain when it happens. And it happens to most of us from time to time.