I sail fin first quite a bit (more as a challenge than because I have to) and I think I do it a little differently than you describe.
I try to tack the board but instead of stepping over the mast to the other side and bearing the nose off, I just step a little ahead of the mast and use the sail and my feet to tip the board straight and move off slowly fin first.
You have to really rake the sail to the side to keep the dirive going in the direction you want and also you have to tip your board a bit to keep the board heading in the direction you want to go.
I think I also initiate fin first sailing by "stopping" a jibe half way around, flipping the sail and leaning it well outboard to get it to power upwith me slightly ahead of the mast.
The big tricks are to get far enough forward on the board (you are facing the back of the board now) and getting your feet spread far enough apart so you can easily tip the board so it corrects back to the direction you want to go.
No, you can go at a significant angle to straight downwind, but you really have to manage the direction the board is going and make lots of little corrections before the fin "bites" and turns you too much so you stall. You also have to keep the rig tipped over to one side. It's very much like sailing out of a jibe clew first.
Practice your clew first sailing and this should help alot with sailing tail first.
You cannot go on a beam reach, of course, but you can go around 30-45 deg. on each side of straight downwind with a bit of practice.
Give it a try.
I'll do some fin first sailing this weekend and give you a bit more on how to initiate.
Hope this helps,