Heater and dash pieces are different. The 250 will need new motor mounts and MIGHT have some clearance issues at the radiator, but you won't know until you do it. That's a nice looking K-20. Keep those "20" badges safe. They don't repop those. I hope you find the headlight covers for that '62. It will definitely make it more unique with the correct grille treatment. You just don't see a lot of '62's. You don't see many K's. And you don't see many 20's. Good for you.
There was a pair of NOS fenders on eBay the other day for around 800 bucks for the pair. That's a good deal.
http://rides.webshots.com/photo/2578304020054213402wSjlLJ