Toxi had a great suggestion in one of the other threads- why not just increase the size of the House?
It mostly fixes the proportionality problem.
The more you increase the size of the House, the more you increase the extent to which the electoral outcome does not match the vote well. If you picked any 10km^2 area and looked at the people there, very few of these areas will have average demographics that will match America's average demographics, because similar people economically, socially, and racially tend to cluster. You get a sorting effect, where each district will tend to be more lopsided than if they were larger with fewer and fewer close district, and social demographics that feature less clustering will receive a disproportionately large amount of representation. In America, that's the Republicans.
(There's a fairly complicated proof of this, but you can sort of imagine: if America was a single district that elected a single person, they'd be D, because America is. If you cut America into two districts, you'd either have D/D or D/R - there's no way to cut it into R/R. If you cut America into three districts, you could have D/R/R, D/D/R, or D/D/D - you can start packing Democratic voters into just one of the districts to create more and more Republican voters. As you increase the number of districts, the extent to which the house becomes dominated by the least packed party increases. This process happens naturally just through population movement patterns.)
So if you increase the membership of the House, you do give more power to larger states, but you also make larger states more Republican in the House at the same time.
As an N.B., this proof doesn't hold if the districts get *really* small - if there was one district per voter, then the results couldn't be biased because if a party got 52% of the vote it is literally impossible for it to do anything other than won 52% of the seats. IIRC, the exact relationship follows Pascal's triangle and there's a formula for it, but I've not read this paper in a really long time.