I don't really understand that 2nd bit. How are you going to end up with the same number of congress people? And if you are dividing up seats by party doesn't that incentives you to cater to the base more?
You aren't dividing up seats by party. You make big districts with at least 5 representatives. Anyone with 1/n of first place votes is elected. The candidate with the fewest first place votes is removed, and you repeat until all the seats are filled.