My dad says 3 weeks is the most I'll be able to handle of Europe for backpacking with a few friends?

I agree with you completely! I have done it twice, but once with a Contiki tour and once without the tour. Have you heard of them? You could go get a brochure from their office, not to sign up, but to use for your argument. Get the info on the tour that is closest to what you want and especially closer to the time you want. This shows that professional tours need this much time to bring backpacking tours through those areas in this amount of time. If you overshoot it, you can come down a little for your dad, and all is good. Like get a tour package pamphlet for 6 weeks, but say you agree this is too long and meet him at 5 weeks.... Go get him, you will not regret any extra day you win! Good luck.