@cfrank The problem of having an exactly proportional result whenever possible is that it drastically weakens the monotonic properties of a method. E.g.
2 to elect
99 voters: AB
99 voters: AC
1 voter: B
1 voter: C
The Perfect Representation criterion would demand the election of BC, even though A has 99% of the support with B and C having just 50% each. And I think that's too much of a demand.
And if you want the result "as close as possible", that pretty much just is the var-Phragmén method. And this has the same problems.
You could specify some sort of convergence requirement. Maybe this could be in terms of maximum variance.