I feel your pain, as a fellow bootstrapper, but a single paid dyno, which will keep your app unidled, is gonna cost you $35 a month. I did run into a bug recently where one of our dynos was being idled even after we paid up, but it has since been resolved.

I'd say just pay them another $35 a month. Considering the miracles Heroku regularly performs as an ops team, it's worth it.