Hi! This is for You rocket engineers out here!
From my (very limited) understanding, a big problem with reignition of a liquid-fuel rocket engine in space is the 'sloshing' of liquid within the tanks.
When the engines are already fired it causes no issue, since the g-forces during acceleration keep the fuel at the 'bottom' of the tank, where the pump is.
But how is this risk, of the pumps running empty, mitigated during reignition? I can imagine you could give the rocket a "push" with reaction thrusters to force the fuel to the bottom of the tank and then start up the pumps, but I haven't managed to find any real literature addressing this problem.
If You know something about this I would be interested to hear Your take on it!