Should focus on keywords with 22,200 searches per month, but for which I only rank 44th, or should I focus on keywords with 480 searches per month, but for which I already rank 7th?
I've always had much better luck ranking for tail terms first. It is very hard for a newer site to rank for competitive high traffic terms. My sites have typically grown into head terms over the course of years.
Focus on creating content that contains both the head terms and lots of auxiliary tail terms. You'll rank for the tail terms first, but eventually move to being competitive for the head terms.