Well, they managed to stay obscure and backwater OTL, and Rudolph was the gosh darn emperor - it takes a while after even that before Austria matters, if i remember correctly.
Sure the Babenburgs could rise, but it would probably take more than this to make that happen given how much they got from Richard OTL.
A marriage might be possible if Richard has any female kin around - Leopold is a duke after all, he's not unworthy of a spare daughter.
And what exactly is England going to do to help Austria?
I like the idea of a timeline where Leopold getting a marriage leads to a Babenburger Austria being something serious and the Hapsburgs being just some random minor noble family in the Alps.
That would be fun to read.
It looks like there's only one possibility of a Babenberger marriage. Leopold could marry
Joan of England. She had a husband, William II of Sicily, but he died without Joan giving him any surviving sons.
She married Raymond VI of Toulouse in 1196, but what we're interested in is December 1192 through March 1193, when Richard was captured.
The thing is, wiki says Leopold was married around this time (to Helena, daughter of King Geza II of Hungary), so there has to be the butterfly of her dying.
Hey... maybe that's what would cause the butterfly; Leopold loses the alliance with Hungary due to his wife's death, and despite already having two children, (one of whom would be the future Duke Leopold VI), he marries Joan along with the massive ransom.
He's certainly canny and ruthless enough, if he risked (and recieved) excommunication for capturing a
fellow crusader.
So I think that's a good bet.
Oh, and while looking for info, I found out that not only was Leopold related to the Komnenos dynasty (his mother was Theodora Komnenos), yet another one of the stipulations for the ransom was the release of
Isaac Komnenos, Despot of Cyprus into Leopold's care.
I could probably fit Isaac in somehow. Maybe he marries a local heiress, and his Germanized Komnenos family branch becomes powerful in Austria? Or maybe he goes off to the Levant in another scheme to become Emperor?
In any case, the Joan connection (with the PoD being Helena of Hungary's death) seems like the best bet.