Much work is already done in committee
Rather than electing representatives from regional districts/constituencies, electing people directly to committees makes sense. Suppose you like candidate A's stance on funding for NASA, but abhor his views on immigration. With regional districts, you elect the candidate as a whole. The speaker of the house and party leaders would decide what committee he would get sent to. In other words, you may or may not have your view on funding for NASA represented by Candidate A, but may end up with him on the border committee that handles things like immigration. Its Russian Roulette. With direct elections to committees at the federal level, for example, there would be 20 seats available for each committee: science, agriculture, social, etc. These seats would be at-large. These committees would be mirrored at the state and local levels as well (in fact, to prevent voter fatigue, an election for 15 committees would do it for all levels. For federal, it would be the average of every local and state level). Rather than having an omnibus budget bill, each bill drafted in the committees would have to match spending with revenue. Committees would vote on bills themselves (majority = 11 members) Vetoes would still be possible (US) by the president, but overridden by 2/3 vote of council (around 13 members). Unicameral would be preferable, but if not, the committees could be the House, while the Senate would exist and look over bills as usual. Of course, riders, pork, and any unrelated items would be struck from the bill (unlike now). Council of all committees would meet up and decide overall budget. It may be equally divided between committees or apportioned how majority sees fit.