If you become a Maryland resident, you can legally buy and possess a suppressor, as you know.
Unless Delaware law changes, you won't be able to take it back to DE with you, also as you know.
This means selling it from MD or otherwise signing it over to someone who can legally possess it. Unless you plan to return to Maryland later, it would seem simplest to just sell it, perhaps on consignment.
Delaware cannot control your actions or possessions outside their jurisdiction, so if you had somewhere you could legally leave it/keep it in MD, you could continue to own it and then use it when you visit MD. I seem to recall some C-III dealers with indoor ranges that would keep your C-III gear for you and let you use it when you came to their facility. This would only be a stop-gap solution if you did plan to return to MD.
If you did continue to possess it in MD after returning to DE resident status, that MAY give you standing to challenge the DE law, in that you have a legally owned item you cannot bring to your home. If this seems like a possibility, contact a firearms-savvy attorney. Feel lucky?