>You cannot have both, unless you're willing to have a legislature that has something like 5,000 people in it, which is not practical.

Australian five-member STV districts beg to differ. As does MMP:

http://en.wikipedia.org/wiki/Mixed-member_proportional_repre...

And DMP:

https://en.m.wikipedia.org/wiki/Dual-member_proportional_rep...

And PR-OAC:

https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2778867

One of the biggest problems we run into is not that there are no options, but there are so many possibilities that people who study the problem in detail end up arguing with each other rather than forming a coalition for a single reform! I also designed a system based on a simplified CPO-STV, but I keep putting off writing it up.