One overlooked electoral reform to decrease the power of special interests in the U.S. political process would be to expand the size of the U.S. House quite significantly, so that legislators cater to much smaller electorates. (More radically, state partition could also be promoted to expand the size of the Senate.) Accordingly, I thought today’s Daily Chart from the Economist was telling:
Of the world’s 22 most populous countries, the U.S. has the second-most people per national legislator.
PILEUS 
Perhaps what is needed is not more congress persons but more time at home for congress persons.
In Texas, the legislature meets every other year for only sixty days. This means legislators are home in their districts for 670 days out of every 730. This leaves ample time to mingle with the constituents.
In spite of such a limited time to make mischief, the state as a whole, delivers more services, enforces more laws, and incarcerates more felons than the federal government. It also spends about half per capita what the feds do.
The State of Texas delivers more services than the Feds? What are you basing that on?
There’s the public schools, the university system, the roads, the police, the prisons, the state guard(not the same as the national guard), medicaid, regulation for the environment and most of the state economy. The feds duplicate some of that but don’t deliver as much per capita or in aggregate. Most of what the feds provide dollarwise and servicewise is social security and the department of defense, neither of which I use currently or likely ever will.
What’s the actual cause-and-effect here? Are you hoping that if there are more congressmen, it will become too expensive for lobbyists to buy the votes they need (like the reform Britain’s rotten buroughs). The flipside is that each congressman will become a smaller operator, who might actually be easier influence. After all, each one will need proportionately less campaign cash.
I think the idea is that by having to cater to smaller electorates, politicians will have to raise less in campaign donations and are less likely to be beholden to large interests. Ease of influence will level the playing field among different interests. I’m skeptical that institutional tinkering of this kind can revolutionize politics, but the experience of states with larger (per capita) legislatures, like VT and NH, does indeed imply that corruption and large interest-group influence are lower in such systems.
In terms of the possible, this also supports devolving more power to smaller governmental units, such as state and local, to empower individual voices further.
In terms of the impossible, we could split the federal government up into different functions – military & diplomatic / protection of the commons & infrastructure / welfare and individual services / commerce and economic regulation – and have separate legislatures for each and separate elections thereof.
We have something like that already. It’s called federalism. Congress has chosen to expand the powers of the government beyond the military and diplomatic and duplicate those other powers which you enumerate, powers which historically were reserved to the states.