I like to start from where we are, as opposed to where we could have been. No sense in pretending we have a time machine.Well, the constitutional limitations on Federal powers means most problems are simply not Federal issues. By preventing the Federal government from having the authority over the issue, the Founders hoped to isolate the Federal government from such a corrupting process.
The Constitution allows the Federal government to exercise certain powers, and denies the Federal government powers not enumerated. If you use the yardstick of last year's budget, then the losers and winners will feel the losses and the wins. I would argue that this is a corrupted measuring stick, however. This leads to our current political situation in which one party screws over the country for the benefit of their donors. Then the other party says, "Hey, we want to screw over the country for the benefit of our donors for a while."
John Taylor of Caroline wrote about this extensively.
If the Federal judiciary would fulfill its constitutional role and negative Federal acts that go beyond Article I, Section 8, the Federal judiciary could insulate the budget process from the pressures of elected office. Were the Federal judiciary to throw out such laws, the elected officials could tell their donors, "I tried to enact your [desired but unconstitutional] program, but those darn judges threw it out. Dadgum it. Can I have some money nevertheless?"
It's a bit late to rely on the federal judiciary to bring about the kind of sweeping changes you reference. Too much precedent to the contrary there.
I think the first phase of the solution lies in addressing the bolded statement above - though also with the recognition that the First Amendment and precedent recognizing money as speech prevents the elimination of lobbyists and such.