Aside from the problem that you mentioned with getting miners to agree on exchange rates, there is also the problem of being able to validate a block some time in the future; you'd have to have definitive historical data for the exchange rate in question going back to the beginning of the block chain to compare against. Even if you were just going to trust the longest chain implicitly when there is a single longest chain, if ever there were forking (and there would be alot of forking because everyone's rules for what a valid block would be different because invariably nobody would agree exactly on what the exchange rate was at a given time), you'd still have to have authoritative exchange rate information going back to the time of the fork.
Yes, I won't verify historical exchange rates. Only when a new block is added that would become the new head of the chain, would I decide whether to accept it or not. Alternatively one could verify the exchange rate in the last 6 blocks (therefore only needing about an hour of historical data). Depending on the bandwidth of your feedback law, data points older than X would be irrelevant anyway.
I don't agree that there would be a lot of forking since the NORMAL condition is for everyone to be connected to all of the exchanges and report some average value. Only when there is some network disruption, would some or all miners not be able to access some exchanges. You could have a generous margin for error on what rates you will accept for when things DO go wrong, maybe as much as 10% variation. Arbitrage should keep exchanges closer together than that. With such high noise in the measurement, the control loop will have to be quite loose, but as mentioned before, this doesn't actually matter. Once traders believe that the control law CAN work it won't actually have to work.
I don't want to get bogged down in implementation details, because I have no intention of implementing. If you don't believe it could be done decentralised, then assume for argument's sake that the exchange rate is being reported by one or more trusted entities, similar to how alert messages are provided on the bitcoin network today. They could misreport the exchange rate, but that would mean the end of the currency, since traders would immediately know that they misreported and lose faith in the system. If they are somehow temporarily prevented from reporting, the network would simply keep going at whatever reward level was set previously. The expectation that rate reports will come back online in future and force the exchange rate back to parity would keep the exchange rate at parity even in an extended absence of reports.