Here's an answer based on my experience.
First, I eat a lot of grassfinished hamburger. When I buy the high fat (therefore, more tallow) my wife and I both noticed a kind of weird film on the top of our mouths just like you mentioned. Very odd and not something I ever notice in the regular grassfinished hamburger. And, yes, it only happened if we waited too long and it got cold. Our answer . . . we buy the regular grassfed hamburger.
Second, I use grassfinished tallow that I render myself in much of my cooking. Unlike Lard, it hardens much faster when cooled and so we need to eat it hot. In fact, in the refrigerator, the Tallow is much harder while Lard is softer. I wonder if it doesn't have to do with the higher amount of PUFA in the Lard than the Tallow, but don't quote me on that. It's just a guess. Someone on here probably knows the answer though. I've never experienced that roof-of-mouth feeling after using my rendered Tallow.
The tallow I make is usually very creamy white and, as I said, much harder to break than the Lard I render. Never used any other kind so can't really tell you how to compare. But I hope that this can help in a little way at least when comparing your tallow to mine.