> we have to run the call in the web process

I know you probably have good reason for this, but this smells like an architecture problem. Whenever you are talking to an external service it is a good idea to have your code laid out such that you can do that in the background. I understand that if you didn't plan enough architecture and maybe even product design to make that feasible from the get-go it is an expensive thing to build, but regardless of who is your hosting provider sooner or later you'll likely need to do it.

One thing I've always liked about heroku, at least in concept, is that it forces you to have good architecture. Some times it is a bit of a pain, but I think this pays off quicker than you seem to realize.