Consider that all ledger entries enter the main ledger as valid, including potential double spends. Then the miners build a separate blockchain of double spends and earn fees. There is no ordering on the main chain. Each miner gets all ledger entries once, unordered, and otherwise participates in the PoW blockchain of double spends.
The double spend causes reverse spend on the main ledger, fees charged to the offending account.
Each miner keeps an unordered set of entries as received, subject to verification by a commutative checksum or crc. An empty account contributes zero to the checksum (is the identity in crc) and can be deleted, when cleared of double spends.
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