This might just be a language issue, because different sources use different words for consistency guarantees.
> Accord only avoids enforcing an ordering (2) on transactions that are commutative
If the committed state in the database records the transactions in a different order than an external observer could have observed them being accepted by the database, then you don't have what Spanner calls "external consistency" - I thought this is what you mean when you say "global strict serializability", but now I'm not so sure.
Cockroach does enforce this property, but only for transactions that touch the same (key-value layer) keys. They talk about this a bit in their article on "life without atomic clocks"[0].
In SpiceDB[1], we take advantage of this property (when Cockroach is selected as the backing datastore) to give us external consistency by forcing all transactions to overlap. This prevents the New Enemy Problem[2], which is what Google calls the problem of transaction ordering when seen from an authorization perspective.
Your description of Accord sounded very similar to how Cockroach works from this perspective, but there may be some subtlety that I am missing. Cockroach exposes snapshots via "as of system time" queries, which can expose "bad" ordering back to the client in future queries - if Accord doesn't allow snapshot queries then I suppose it wouldn't be an issue.
[0]: https://cockroachlabs.com/blog/living-without-atomic-clocks/...
[1]: https://github.com/authzed/spicedb
[2]: https://authzed.com/blog/prevent-newenemy-cockroachdb/