I still prefer (in untested theory) the following:
Use MP to accelerate or decelerate. Turning costs <speed> MPs. Sideslips are interchangeable with forward moves. There is no special "Agile" or "Nimble" designation, but overthrusters exist as per previous editions of Starmada.
This system has no restrictions on when you can turn or sideslip. If you have 15 MPs, you're welcome to come about in one turn at speed 5.
Sideslips are, as David notes, necessary to eliminate hex grain issues; I believe that, using hexes, your facing/heading is an approximation, so you should be able to move in any direction that is within the approximate arc. It is technically more correct to not allow consecutive sideslips (so the approximate arc is 60 degrees wide rather than 120), but I'm willing to trade that amount of realism for lower predictability and simpler plotting.
As for fighters and other small craft, I'd prefer for them to just have 10 MP/turn with no inertia. I realize that a ship with a head start can therefore outrun faster fighters, but with a little handwaving this can be explained as a simulation of the fighters' limited fuel capacity. Since fighters are so fragile and simple, keeping track of speed for each flight seems like too much work.
I believe this has all the advantages of the system David proposes, while being simpler.
Counterarguments? Playtests that reveal fatal flaws?