IANAL. I think that your assessment is correct in the consequences but not in the letter: your source code does become GPL but if you don't distribute the binary and only use it on your servers nobody is entitled to ask you the source code. That would happen with the AGPL license.

Same thing if you make changes to Ghostly itself and don't distribute the binary. Those changes are GPL but you can keep them to you.

If you are working for customers and the IP of the software is yours but the servers are theirs, that is an act of distribution and the source code must be available. For sure customers can ask for it because binaries are distributed to them, maybe everyone else can ask it too. This is the same as GPL code on set top boxes or other devices.

If the contract states that the IP belongs to the customer, the source code is theirs but nobody else is entitled to ask for it because there is no distribution.