Building your own authorization/authentication and integrating with OAuth is pretty trivial, maybe a few hours if all you need is simply logging people in. Same with a CRUD CMS that'd replace refinery -- you're collecting complexity for a more rich feature set out of the box.
Rack Rewrite isn't really that complex, though Carrierwave+Fog is a complexity layer, if Fog is anything like S3 you could just be posting directly to a REST api(adding complexity in client-side JS -- my favorite kind of complexity.)
Unicorn is slightly more complicated to manage than Passenger, but, apparently you needed to serve fast clients and work on disk a lot? Well, can't be mad about what it buys you.
Honeybadger, Foreman, and New Relic are pretty much DevOps burdens, you'd probably have some form or fashion of this complexity in any web-based app, ever. AMQP is a standard, most people would need a library to interact with it -- this is sort've akin to complaining that you need a library/gem for JSON.
I wasn't even sure you needed heroku as a project dependency -- I though you just needed it locally because it acted like a CLI to their service.
Also, Sinatra is it's own framework, having nothing to do with Rails. And it certainly wouldn't trade out a lot of the dependency complexity you're dealing with.
Really, you traded simplicity for rich features out of the box. Hopefully you took the time to figure out if you actually need those features before integrating them with your app. Also, Refinery's Engine architecture is kind've hair brained.
(P.S. on chrome 24.0.1312.57 and Mountain Lion the dynamic length comment box on this blog is totally fucked.)