> modify the fundamental nature of the House of Representatives such that a representative's voting power is proportional to the share of the vote they got.

Germany does that. They have districts, which get to send the winner in each district to parliament. But these only account for a part of the total seats available.

The others are filled up from a party list in such a way that the proportions are equal to the proportions of the votes.

That way you get the best of both worlds, you have representatives that have a connection to each district, but you still have the distribution in parliament that represent the actual distribution of the votes.