I think the event chain that gets you there is very long.
I did it once and I remember it took quite a while. Arthas' sister was already married, well over middle aged and had like 7 kids when I finally took the throne.
Spent 10+ years just as a very powerful vassal to the Lich King.
I'd say keep going, and make sure you follow the canon course of events: Culling Strathholme, burning the ships etc. Should happen eventually. You can always try and assassinate Ner'Zul too. Once tested with console commands and as soon as he dies, and if you're the heir as Arthas, you get the event where you ascend.