I've just converted the .gems file to Gemfile (with lock). After that the initial heroku push went just fine.
Moved .gems into Gemfile
Thanks, Kristoffer, it solved my problem too.
Alexis, it would be great if you could accept this pull.
I almost gave up because of this inconsistency. And if I didn't find this here, I was surely going to give up.
I'll close this. Seems like this project is d.e.a.d.