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What caught my attention is this: But none of them will be able to prove it.
Sorry, those who give big money will find ways to document that they have shifted money to a particular account.

William L. Benoit described the problem very well:

The major problem in campaign financing is the fear that some donors expect their contributions to be rewarded with political favors, votes or decisions that candidates would not have made absent those donations. We worry that our elected officials are for sale to the highest donor.

Incumbents win re-election to the House roughly 95% of the time, and to the Senate roughly 85% of the time (Open Secrets).

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... for equalizing the amounts of money candidates or parties spend on campaigns? It seems important to try to develop the playing field by making money from any source is less of a factor in choosing leaders for our nation.

In 1996 several colleagues and I argued for a limitation on the source and size of contributions to parties (i.e., an elimination of soft money) in exchange for the freedom to spend hard money as they deemed most efficacious. This recommendation did not become part of BCRA and it is no surprise that party independent spending in presidential and congressional elections has exploded. In the two elections before BCRA, party independent spending totaled $3,866,977 in 2000 and $3,645,408 in 2002; after BCRA, the comparable figures were $264,524,078 in 2004 and $223,746,652 in 2006.

Candidates either must be wealthy enough to finance their campaigns, or must raise huge amounts of cash from either the public or special interests.

These political organizations are not regulated by the Federal Election Commission or by state elections commissions, and are not subject to the same contribution limits as PACs.