I guess it would be wise if you chose to focus your energy on one thing, DP, AC, Op. jumping around makes you look like you're in it to make whatever you can.
Just because you join the union as a DP doesn't mean you'll score projects as one (as per your post). a lot of union members seem to work their way up from the bottom (as they should) but it doesn't mean that DP's don't come out of the woodwork without previous camera experience in a different capacity; at least this is what my father explained to me.