Here is what I propose:

• Every block in the block chain only pays out 90% 99.9% of its block reward. The other 10% 0.1% is kept on reserve in the block.
• A second "balance" chain is created, which consists of transaction chain blocks hashed in a tree along with the usual nonce and a hash of the previous balance chain block.
• Each balance chain block holds the balance of every non-empty bitcoin address up to the point of the last transaction block included.
• The balance chain difficulty is 100X 1000X the transaction chain difficulty.
• The node that solves a balance chain block recieves all of the reserved block rewards from the included transaction blocks.
• In this manner, over time old transaction blocks can be forgotten since the most recent balance block plus the most recent transaction blocks are all that are needed to verify transactions. To keep the integrity of the network, of course, more history should be saved, but we probablly don't need more than a few thousand balance blocks while still being very secure.
  In this manner, the only data required for each full node would be: (1) block headers for all balance blocks (2) the most recent balance block (3) transaction blocks that occurred after the most recent balance block.
  

Do you think this scheme could work? I'm not even remotely an expert on this stuff, so forgive any glaring errors. Thanks!