It seems as though Elder Primals are a different beast entirely. The name itself may well be a misnomer, as they are completely different from what we know as "Primals." Bahamut and Midgardsormr are Elder Primals, which from what I can tell, serve a specific purpose in regards to the balance of aether in Hydaelyn. Midgardsormr's corpse can still be seen in Mor Dhona and...
<Binding Coil spoilers>
...Bahamut is still lingering in pieces, but very much alive.
So it would seem that Elder Primals do not disperse their manifested aether like the Primals do, nor do they live in on in the Lifestream, as it is thought that the Primals do. I do not believe Midgardsormr can be summoned again in his former form, nor do I believe that he would retain anything that resembles his previous station as guardian over Silvertear Lake (meaning, whatever that made him special and specific to do that job is lost and probably would not be able to be recreated through a summoning).
I think, if I am allowed to make a FFVII parallel here, that Elder Primals are Hydaelyn's "Weapons." Intended to do good and protect, but just wind up mucking everything up and can't be replaced.
EDIT: Although, at the end of all that, I just thought of Odin, which blows my entire logic train out of the water. Oh well. I'm leaving it there. For posterity!