DIST would be what you need. You're correct in that replication will not help you.
Regarding the read-only nature of the map, ensure you have L1 caching enabled as well so that you can minimise the cost of repeated lookups on a single, remote key.
Keep in mind that as of ALPHA6, DIST is pretty unstable. Trunk is a bit better and I hope to cut a far more complete and stable version as BETA1 soon.