Q: How is this different versus the propellant(s) in any liquid-fueled conventional rocket in use today?
A: Not at all. Propellant sloshing is part & parcel of all liquid fueled / liquid oxidizer rocket systems. It’s a solved problem. Next.
Good point.
This is another reason why using a solid ablation material – plasic or ice – is preferable. No sloshing. No pumping needed.
It also doesn’t have to be at cryogenic temperatures, as an H2/O2 rocket would be, which simplifies your entire fuel handling process.
Even the versions that use ice rather than liquid water probably wouldn’t have to be that cold.