1. Heroku is expensive. Odds are you can get the exact same virtual/hardware specs with a cheap VPS from Digital Ocean or Linode or any of various other providers. It'll require a tiny bit more setup and configuration on your part, but it'll save you money. You could also consider shopping around lowendbox.com and lowendtalk.com to find the best current deals. 2. Optimize your application so that you won't need to sc…
That said, I wouldn't trust lowendtalk.com too much if you want stability. If you are seriously contemplating a $300 budget, you can get away with $60 on Linode or Digital Ocean and have much, much better stability compared to some of the providers there. If stability isn't a big issue for you [e.g. 95% uptime is okay] then you can go with those providers.
That said, I wouldn't rely on a donationware model to bring in enough money unless it is less than $100. I know some sites that do function that way (mainly forums with strong communities) but generally they can't raise more than $100/mo reliably.