$12k difference is not a lot when you're talking about where you live, when it's further than a day's drive away and you're not intimately familiar with the new town. It's really more insurance in making sure that $200-$500k+ investment down the road is the right one.
Assuming housing prices stay the same...that investment buys you time. You get to know the new area, neighborhoods, really look around and pick where you most want to live, and wait for the right house to come available. You can scout for the spots that check all your boxes, not just the house itself, but proximity to amenities that are important for you personally (i.e., walkability/drivability, distance from highways, to hospitals/parks/shopping).
You are in the easy-day-trip range for the new location, so you could do the work in a lot a lot of short visits instead.
The downside is you spend a year in a temporary location. A year in a bit of upheaval, maybe also some stuff in storage. If you have pets it's also a bit of a challenge.
But $12k would not be a factor for me. Incidentally, that's about what Zillow says my home value has lost in the past month. The headwinds are against further increases, and most areas should expect home sales to slow. I'm not much for gambling, but I think selling today would net you more than a $12k difference (in your favor) vs. selling a year from now. If that also holds with the new place...win win!
Of course it could go the other way - you sell now and then in the next year things shift again and start to go back up. That's why you have to be ok with whatever happens and focus on being where you want to be.