Sore neck in backstroke

I've recently decided to put more backstroke in my workouts. I started TI swimming in late 2015 (after a 40 year layoff from swimming) and am generally happy with my progress in freestyle. Even back in the 70s as a teenager, I struggled with backstroke - only did it as part of IMs and had no good coaching on how to do it better.

So what I'm noticing is that when I swim backstroke, almost immediately the muscles in the back of my neck (really in the lower part of my head), are incredibly tense. I can float on my back with no tension, but the minute I start to kick, the tension starts. Right now I'm trying gentle kicking (arms above my head in streamline) with a total focus on relaxing my neck, and I'm not making much progress.

I'd like to come up with a 400 yard drill/full stroke sequence that I can work into my workouts, but so far, I don't think I can come close to this.

Any suggestions?