What would've happened if Czar Peter III had been "abducted" to Stockholm and St. Petersburg? The Swedish throne was far better established, ergo he would probably marry someone a little more important than Sophie of Anhalt-Zerbst (therefore no Catherine the Great).
Also, could we perhaps see Finland electing him as king, on the condition it passes to a second son, or in lieu of that, to the nearest male relative in the house of Holstein (Adolf Frederik OTL King of Sweden).