One thing to consider is that there are no more members of Tiber's bloodline left, and least none that the general population would have known about, otherwise they would have been assassinated. In scenarios like these, in our own history, there are only so many options:
1. A non-royal blood relative of nobility is raised up
2. A theocracy takes over
3. An outside power sweeps in.
4. A pretender claims to be of royal bloodline
5. A warrior hero of local renown is asked to take the throne.
I'd say use all five of these as the main conflicting interests. More expanded ideas follow:
Scenario #1:
A non-blood relative could be something like this:
Royal parents Noble parents (non royal blood) || || ||Male (royal blood) = Female Male (uncle to royalty, though not of royal blood) ||Royal off-spring
So in this case, you have an uncle of the heirs who was the brother of Uriel's wife. This does not make him blood (and therefore not assassinated), but certainly would elevate his position and make him a legitimate claimant to the throne. This person is most likely on the council.
Scenario #2:
The ruin of the empire via Oblivion is considered to be a failing of modern religion. It opens up for a new cult that (falsely) takes credit for the banishment of the Oblivion invasion. The popularity begins to spread, and the key leading figure starts making a push to fill the vacated seat of power. The claim may have more strength if said leader is also on the council.
Scenario #3:
As presented, a warlord or some exterior invasion force plans to sweep in and either just ravage the land for what is left, or take over the seat of power. This could also be arranged from the inside, and could be connected to one of the council members.
Scenario #4:
Someone is presented as an illegitimate son, but still an heir, to Uriel Septim. The pedigree is documented, but since both the parents are dead, and all there is to back up the claim are the heresay of servants and those that were "in on the secret". Ideally, this should be a child, and conveniently, a member of the council who is acting as his protector, will naturally rule the kingdom until he comes of age.
Scenario #5:
The main character, the Hero of Kvatch is suggested. With the threat of war from outsiders, cultish non-sense, and who knows what else, who better than the man hand picked by the Emperor who manages to save the Empire from complete destruction - and has the Blades on his side to back him. Surely a member of the council would put forth that name, especially if he will take care of the "day to day" business of the realm since the Hero will be out busy doing Hero stuff.
So now you have a great dynamic of multiple factions, each with a supporter from within the council, all making a bid for power, with Ocato caught in the middle. I don't know how many members of the council there are, but if there are at least six, you are golden, one for each scenario, and Ocato trying to juggle it all.
Conceptually, it's an intriguing idea, but it's going to take a lot of work to pull it off.