Hmm - some interesting questions off of this.
Doing some research with the aid of the excellent A. N. Wilson, he suggests that in 1817 the Duke of York was "deeply involved with a middle-aged mistress" - something that might be a road block if only I could figure out who she was? The Duke of York seems to have cut off relations with his only famous mistress, Mary Anne Clarke (she of the commission selling and the caricatures) in 1811, so I don't know if this is just some confusion with dates on Wilson's part?
Also, more incidentally interesting, Wilson suggests that the Duke of Kent was considering a princess of Baden (probably Amalie, born 1795) as an alternative to Victoria of Saxe-Coburg-Saalfeld. (Amalie of Baden did marry in 1818 though, putting her out of the picture as a later contender).
Some more points - a biographical memoir of the Duke suggests that
firstly - the Duke had serious "spasmodic" (I think respiratory) issues for the last four years of his life that made it hard for him to breathe lying down, and that he was essentially an invalid since 1826 (so I don't know if kids after 1823/4 are terribly possible)
secondly (and this is also an unrelated thing, but George IV apparently almost drowned in 1820 - this would have made Frederick, King, although it's still doubtful whether he would have been any more likely to remarry because of this)
Just based on the health issues - I'm increasingly skeptical whether Feodora would have worked - the time window to get married and have a child in 1823/1824 is either slim or non-existent - I'm not rejecting the idea off hand, just wondering if there are any other candidates people can think of (I can still see Auguste of Reuss getting in one last matchmaking success with the Duchess of Kent's cousin, but who knows) - or if we really do have to thread the needle on this one?
I can't find anything on any other major mistresses after 1811, so I am going to make the assumption that either we're missing key information or he's wrong, but in this case I'm going to go with the other person being wrong just for the sake of the scenario. Who knows, maybe Frederick was shaking up with some nice older lady in the last 1810's and would never have dreamed of marrying again. But let's just say he's available.
The health thing is something I can't find much on, but then again I didn't look very hard. However, if that is an issue, he's free fro 1820 onwards, so if we have Elizabeth of Clarence survive until late 1822, then early in 1822 we have the marriage, and in late 1822 we have Prince Frederick George Charles of York, with his mother at the tender age of 15. By 1824, we can have the two sons be born and the Duchess is a widow 3 years later, at the age of 20.
Prince Frederick, Duke of York and Albany (b.1763: d.1827) m. Feodora of Leiningen (b.1807) (a)
1a) Frederick George Charles, I of the United Kingdom (b.1822)
2a) Mary Elizabeth Anne of Clarence (b.1823: d.1826)
3a) William Augustus Octavius, Duke of York and Albany (b.1824)
Now we have something something interesting to consider here. Reportedly, Feodora was a handful of a young woman who loved to party and had to be married off to keep her reputation, as her mother saw it. Now she can't be married off if her son is the next King, can she? So do we see her partying it up at court, separating herself from her mother and keeping the power behind her sons entirely in her hands. In fact, if she truly does manage to keep herself seperate from the Duchess of Kent, she might be the one to shut down marriage talks for a match between her sister and son.2a) Mary Elizabeth Anne of Clarence (b.1823: d.1826)
3a) William Augustus Octavius, Duke of York and Albany (b.1824)