Actually it occurred to me that if you think about it, a Seeker is a Spirit Warrior. I'm not entirely convinced by the explanation that Cassandra gave of them being made Tranquil by their prolonged meditation but the end result was that a faith spirit touched her mind and gave her the special powers that Seekers have. Of course in game they just gave her the Templar spec which is nothing like what Seekers are meant to be able to do. However, the most useful thing with regard to Tevinter is that the Seeker spec protects from possession and blood magic mind control. They don't have actual Seekers (or proper Templars) in Tevinter but that is no reason why you couldn't have something similar, just with some other spirit acting other than a faith one.
The examples I gave above were just off the top of my head as explanations for the acquisition but it doesn't have to be that complicated. You simply have to have an order of warriors where their training is similar to that of a Seeker, in other words they spend a period of time in mediation and then someone encourages a spirit to touch their mind, which is what I assume must happen with Seekers considering they are meant to have emptied their mind of everything, so you would assume there would be nothing to attract a spirit. I assume with the Seeker the spirit must stay in touch with their mind because that is the only thing that would give them their special skills.
So the player does not have to be a special snowflake. I'm not suggesting it is something that is unique to the PC and no one else. You just have to come up with the right explanation for it. According to the lore in their Core Rule Book you do not have to be struck down and resurrected to be a Spirit Warrior, just have a partnership with a protecting spirit. Tevinter seems just the sort of place to explain how such a thing might have come about, since they have a much more positive view of these things than southern Thedas does and so likely to have come up with something. If nothing else, may be Seeker Lambert working with Divine Urian might have given the latter some ideas.
With any luck they will come up with some totally new warrior classes for Tevinter. They certainly can't use Templar because we have been repeatedly been told that Imperial Templars are really just normal soldiers who work for the Imperial Chantry. That certainly narrows the field a bit when it comes to classes they can use, if they stick to ones already introduced. You should only really be a Reaver if you belong to a dragon cult. There was that strange class of warrior, whose name escapes me for the present, that Marius belonged to, so may be that will be introduced to take the place of Templar.