So questions to your proposal:
1) You make corporate political donations illegal, but that's pretty specific to a single class of interest group. What about those that regularly act in opposition to corporate interests, such as unions, environment groups, consumer groups? Your point 2 seems to imply they would be included, but why are you specific here as to the prohibition? Or do you propose to treat different association of people preferentially and on what basis?
2) Again you're specific to certain kinds of interest groups but this time leave out corporations when granting permissions. Again, do you have favored classes of associations of people?
3) How do you police such a thing? How do police communication through surrogates or the thousand other ways creative individuals seeking rent or hoping for regulatory capture will bypass "communications with the outside"? Isn't this the sort of creative thinking that caused problems with McCain/Feingold and the like? If you accept greater regulatory involvement from the state, the greater the rewards to those that can gain the ear of the regulator. Risk/reward continues to skew to creative evasion.
4) What makes a neutral group neutral, and, in some way, can there ever be such a thing? Don't get me wrong, I don't know of any instances of the CBO outright gaming information, or releases, etc. for clearly political purposes (nor have I studied the question). However, CBO Director is still appointed by the politicians. What if one political interest group captures congress and decides to politicize the CBO since they can't get sufficient outside support for their position under your proposal? Do you politicians like Trump would do such a thing? Even if we put those sort of hand-wavy humans-are-humans arguments aside, elected politicians are ultimately beholden to their constituents regardless of the CBO position; CBO says we spend recklessly on the military (or if then that sort of thing) a big military district politician will very much ignore that advice. I expect your funds for increased staffers results simply in increased "independent" research supporting whatever position a given politician wants to hold for whatever reason.
Unfortunately, I still think I'm on the right track and that just about any solution that doesn't somehow require the political class, their staff, and families to be quarantined into some forced monasterial existence cutoff from the outside world, seems corruptible.