Create datasource type variable and configure it so that it will select exactly that one datasource by name, which you need. So you can have my-prometheus-org1,my-prometheus-org2,my-prometheus-orgX and:
Then used that datasource variable in panels.
All orgs can have the same dashboard now because that variable will select exactly that datasource, which is available in that org and which is matching conditions. No need to play with datasource uids (they can be completely random now - you don’t care with this setup).