Somewhere you need an lox and methane inlet to the currently lit raptors that does not experience transient no fuel events. Such events would create situations of incorrect fuel ratios, and fluid hammer within turbo pumps. Ideally hot staging would be completed without a negative acceleration event, thus the fuel would not slosh .

A simple mitigation method might be to allow for cold stage separation, allow for a period of free fall, use a fairly simple and weak cold gas thruster to accelerate the body forward and thus the fuel to the bottom and then relight the raptors.