These are the problems you have with any Django app as you learn to scale it, they're not inherent to Tastypie. They're why prefetch_related and select_related exist, you're Doing Things Right.
I wish that I had a better response for this. I don't. Scaling is hard. It's work, It's not usually magic and you have to understand a lot about your system to get it right. Peppering in a few cache statements and figuring out the proper querysets isn't that bad. I know that I can't be seen as an impartial observer in this situation since I commit to Tastypie, but I got involved with the project because it did this stuff right. If you've got any suggestions on improvements I'm all ears and my email is in my profile