"It would sound fake"

Even granting all of that, there's the moment itself. You imagine saying "thanks for laying the table" and it sounds ridiculous. Stilted. Like something from a training course. Your partner would look at you as though you'd been replaced.

Two things about that. The first is that the feeling you're having is the forecast Kumar and Epley measured. Expected awkwardness. The writers in their experiments expected awkwardness too, and the recipients, on the whole, didn't feel it. The awkwardness is real, but it's yours, it's in advance, and it doesn't cross the room with the words. What crosses the room is the content, and the content is that someone noticed.

The second is about what makes something sound fake, and I think it's vagueness. "You're wonderful" sounds fake because it's a verdict with nothing under it. "Thanks for sorting the post, I'd been dreading that pile" doesn't sound fake, because it's about a pile of post that was there and isn't now. Specific thanks can't be performed. It can only be said if you saw the thing, and the seeing is what the other person is responding to. They're not being told they're wonderful. They're being told the post was noticed.

There's a small study that speaks to what a thanks does to the person hearing it. Lisa Williams and Monica Bartlett, in 2015, had participants receive a note from someone they'd never met, either with a line of thanks for a favour they'd done or without. Then they measured whether participants would give the stranger their contact details to carry on the relationship. Those who'd been thanked were more likely to. The path ran through warmth. The note of thanks made its writer seem friendlier and more thoughtful, and that's what made people want to keep in touch. It's one study with a modest sample, so hold it lightly. But it fits the larger pattern. Thanks doesn't read as performance to the person receiving it. It reads as warmth, and warmth from you is something the people around you may not have had much of, however much of it you feel.

So yes, the first few times will feel odd to you. Say it anyway, keep it short, keep it specific, and watch what happens on the other face rather than in your own chest. The evidence says the other face is where the truth of it is.