It appears (from the writeup) that you are unaware of sybil attacks?

The graph of transactions in bitcoin already functions like what you describe (except 'accounts' are single use txouts); Bram Cohen likes to call Bitcoin without the blockchain "bitpeso".  In Bitcoin the blockchain is overlaid on top of "bitpeso" to resolve "complex forks" (using your language) in a manner that allows someone to join the network and know which resolution is authoritative in a way which is both robust to sybil attacks and does not require membership (because a membership process would create control over the system).

In your description you appears to liberally conflate forks and double-spending.  In Bitcoin, double spending a traditional txout requires malicious behavior, just as you describe.  Blockchain forking in the absence of double spending is benign and no different to the "multiple resolution rounds" you mention from your resolution protocol but fail to describe detail sufficient to permit any analysis.