My suggestion would be to attend some of the conferences where people present the type of work you're interested in doing, even if you have to pay your own way. When I was finishing up my Ph.D., I wasn't 100% sure of which of two directions I wanted to head for a post-doc...somewhat related, but not entirely, to my Ph.D. work, so that's what I did, I paid my own way to some different conferences. Why? Because I had the opportunity to meet the people I would be applying to for post-doc positions, so I wasn't just a random application showing up in their mailbox, and because I got to see what current work they and their students/post-docs were doing to decide if it really did interest me.
I got lucky that THE person I wanted to work with who had research that fit both of those fields had a position open and funding available. I had to beat out three other people in interviews, but that was relatively non-competitive at the time.
And, in the irony department, the other person who I had really wanted to meet while at one of the conferences, but was a no-show (I met and partied with several of his students, but didn't manage to meet him...his students were there on their own that year) ended up being the person who hired me as a research asst. professor in his lab a few years later. I was unaware of it at the time, but he was also a former student of my post-doc mentor, so we ended up eventually meeting through that connection, and doing research together anyway. It ended up the best of both worlds...both people I was interested in working with I ended up working with (I joke that it was a rather incestuous research family).
Anyway, the moral of the story is that if you want to work with people who are doing research substantially different from yours, you will have the most success if you find ways to meet them before applying to work in their labs. It is very common for people to change fields between a PhD and post-doc, and I would in fact encourage it as a way of broadening your background and seeking bridges between those fields as a potential niche for your own independent research when you are looking for a faculty position.