I'm 5'9ish and my old boy is just barely 15hh. I just this week purchased a 15'3 2yr old - I want a jumping horse - but my old boy, a Morgan, is a perfect size for me for trails and hacking, western riding - basically anything except jumping. My dad and boyfriend (who are both about 6ft) also ride him, and he is totally fine.
What I'm saying is - I wouldn't worry about rushing out to buy a big horse. I understand wanting to "upsize", but you won't outgrow your 15hh guy in any real hurry. Take your time looking for the horse you want.
As for draft crosses, a lot of my friends have them - one has two perch crosses and another has a perch X fjord. They're all lovely riding horses - my one friend even jumps her fjord X (although I'm not sure I'm entirely on board with that, but that's a different discussion).
Good luck in your search!