Smart way to do it, but it will set you back $0.5/month. You can likely do it cheaper with Lambda and API Gateway, but you'll have to invent the secret sauce yourself.

I'm always a little surprised when there are short comings in IAM like that with route53 and records. It seems like a natural thing to be able to control, but for some reason you don't have resource level controls on hosted zones. It's all or nothing.