Meh. It certainly wouldn't hurt to get comfortable with the board backwards, but I wouldn't say it's necessary to have it on lock before you shove. I had never ridden with the board backwards before I landed my first shove. I just threw it, got my feet back on, came down, and used my had on the wake to balance me out and keep the board straight. Once you throw it and get your feet back on, make sure to keep your knees bent. That'll help you stay in the pocket and hopefully slow you down if your headed out back.
I'm not familiar with boards that have both a tail and nose fin. I'm sure they exist, but I don't see them too often. It's not necessarily just a fin that would help you while the board is backwards since they often have different thicknesses in the tip tail and the rocker breaks at different points. A fin would make you feel less squirly, but it wouldn't be the magic cure for falling back.
The main thing is just give it a shot. You can theorize everything before hand, but sometimes you just have to go for it and see how it goes. Bring a camera long so you can see where you went wrong as well. Get speed, legs bent, throw the shove, get your feet back on, come back down knees bent, and use your hand dragging the wake to keep you straight if needed.