AHC and WI: Habsburg Sweden

This is inspired by an EU4 playthrough, but I was thinking about Sweden being a Catholic country under the Habsburg dynasty. My POD is that the Reformation in Sweden did not happen and Gustav Trolle dies prematurely before Gustav Vasa comes to power.

Now that Sweden remains Catholic in this TL, in a POD after 1523, what are some Habsburg matches for Gustav I? And how can Sweden be ruled by a branch of the Habsburg dynasty from there? How would a Habsburg Sweden impact the country and Europe as a whole?
 
Gustaf marries Hedwig of Poland since there are no religious issues to prevent the match. He and Hedwig have a couple kids (most of their sons die in infancy, save one, TTL Erik). In a double match Erik marries the epileptic Elisabeth of Austria while his sister marries a Habsburg archduke (maybe Ferdinand II?). Erik has no kids and Ferdinand II succeeds in right of his wife as ruler of Sweden.

Although, TBH, wasn't the throne of Sweden elective at this point? I seem to recall there was some iffiness about Erik XIV being an elected king when he proposed to Queen Elizabeth
 
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