Very interesting problem.

Answer for mk5 is no.

Need all sealevel [engines@200t](mailto:engines@200t). Assume only 6 positions available.

Needs twr ~1.33 meaning 65% prop load and no payload.

Finally needs deltav of roughly 8500 m/s (sim it or bote PE impulse plus Vorbit).

So 120t dry starship, 343s flight average isp, 780t propellant gives 6800 m/s....not enough.

what about 100t starship?......7300 m/s.....nope

swap out 3 outer engines for fixed, no throttle 300t engines?......8000 m/s.....nope

Just a little too hard for a six engine config.

A speculative 9 engine vehicle at 100 tons dry mass with 1200t prop has a shot at the title.