After thinking about for a couple of minutes, I think that the Dolphins should simply abandon their special teams. Look, if they're not going to put any effort into it, why bother even having them at all?
They could release Fields as the punter, and simply never punt. Then, when the other team punts, they can play defense against them, and just let the ball bounce around, and start there. You don't need a field goal kicker; always go for it on fourth down, even in close, and you can go for two. On kickoffs, you have to have someone out there -assuming you score- so you could just squib everything, or simply kick out of bounds and give the other team the ball at the 40.
The only thing is that you'd have to have a returner. But whoever he is, he can always down it in the endzone, run out of bounds, or call a fair catch.
It seems like a better alternative to me if you really don't want to try out there anyway!