So, I'm going to say something that's going to get a lot of flack from people on this thread... but I'd actually like to see the Warden in a DLC one last time. I think a nice little Mark of the Assassin length quest, that begins with us establishing basic things about the Warden before meeting them; and ends with a decision to either kill them off or have them ride off into the sunset, would be a nice bit of content to play.
You don't really need to have all the different voice actors return - they could just give us a choice between 2 voices during character creation, similar to how they did the Inquisitor. Sure, it might be a bit offputting at first that they don't have the same exact VA as in Origins (then again, all they really ever did were stuff like battlecries and such) or the voice you imagined them having. But giving us the choice between at least 2 voices should help it feel like we actually have some say in how our Warden sounds. At the end of the day though, I personally don't think what their voice sounds like is the most important aspect of the character.
The biggest obstacle would be their personality. What kind of person were they? Were they serious, or funny? A jerk or a doo-gooder? Were they Andrastian/believed in the Elven Gods, or were they not religious at all?
Those sort of things though, as someone else pointed out, can be covered rather easily with a conversation before meeting them. Have the Inquisitor say something like "I heard the HoF was a stick in the mud" or "I thought the HoF didn't believe in the Maker/the Elven Gods?" in a conversation prior to bringing up the CC menu.
Someone else pointed out that not all of the specializations from Origins are represented - which is true. I kind of feel like, though, if we're going to be getting post-game content we'll probably be getting new class abilities at some point as well. As it stands, mid 20's is the soft cap on levels. That's enough levels to fill out 3/5 trees. Because Warriors and Rogues have to choose a weapon style, and we can't switch between the 2 that pretty much means that one of those 5 trees is going to be useless anyway. So if we're going to be getting more content, we're probably going to reach a point where we are going to be forced to dump points into abilities we don't need, because we've gained too many levels, and there aren't enough abilities.
If this is the case, then adding a new tree for each class would be a pretty good idea to keep people interested in leveling up. These trees could have abilities in there based off of the specializations that weren't included from Origins. Rogues could get access to Ranger-like abilities. Mages could get shapeshifting skills. Warriors could get Spirit Warrior-esque attacks.
Doing this, if you give the Warden access to the abilities from every specialization and every class tree, a player could certainly create a close approximation of their Warden's build from Origins.
Will it be perfect? No - but it's likely that their fighting style has changed a bit in 10 years. IMO wouldn't really need to be 100% spot on - just something close to it.
As for the whole 'what about if our Warden is dead?': it could be that we get the Orelsian Warden if the HoF is dead. Again, we could choose their class, change their appearance, and define their character rather easily.
Obviously this all isn't a rundown of what I think will necessarily happen. It's just a way I feel they could tackle certain obstacles. I personally don't see a Warden DLC as something that is doomed to fail. On the contrary, I think it could be something rather spectacular. Provided it is used as a send off for our Warden, and an opportunity to give them a 'happily ever after'. Keep in mind, the only Wardens who actually got closure in Origins were the ones who romanced Morrigan and went through the Elluvian together. All the others just sort of disappeared under mysterious circumstances - leaving their LIs behind. We do find out why the Warden went missing in Inquisition - and while it gives the impression a happy ending is possible, IMO it also hints that the Warden has one more adventure to go before that happy ending. 