I think I’d probably be playing/submitting F1,F2,G1 (G2) as standing orders and presume that if you get a stone down after all your stones are captured that because it’s still the same round you’re still in the game.
Unless there ends up being another productive move/block on the board.
I still think it’d be better for vsotvep and martin to try to capture le_4tc. Imagining red’s stones gone, they could probably nearly halve the board. I think if martin gets captured, probably something like c6 with be a big decider on which way the territory goes. le_4tc is probably close to half the area already though if white gets captured.