Sounds like you need to make some European friends, like the Ottomans, Russia and the Commonwealth. I wonder if you could join the HRE if you managed to get a foothold there first...
My other idea would be to somehow become Christian so you can start marrying off to Portugal and some Italian minors in hopes of getting a PU.
Can't join the HRE, you'd need your capital in it, and you can't move your capital into the HRE. Guess I'll try making some friends regardless, but I can't imagine it'd be hard to have them stick around. As far as Christianity goes, I was hoping I'd be able to convert, but no such option has presented itself.