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The biggest thing to consider with NFS is the bandwidth between points. Any modern hardware will be able to handle some pretty heavy traffic over NFS, especially if it's doing just that (like a dedicated dumb file server). Unless you're getting super-crazy and doing massive segmentation over tens or hundreds of exports your only limit is going to be the inter-droplet bandwidth.

Heroku is tough to justify, expense-wise, unless you're a startup looking to set your Rails app up quickly. IMO, it's far easier and cheaper to manage a PHP DO box than trying to do it on Rails (apps that are constantly-running processes like Ruby/Node apps are, IMO, best fit for Heroku).

As for the FS, I believe you can do what you're describing with DO Spaces or Volumes (I believe these are just NFS mounts). I haven't done that bit, but I'm guessing it's fairly simple like most other DO things. DO tries to make it so your droplet is customizable. I think if you just create a droplet in a datacenter location that allows volumes, you can add space to it as you need:

One thing that can't hurt is to email the DO support with your needs and ask if that's something that can easily be done with DO. They'll be able to let you know.