You call this variant "sesqui-eyed go", which appears to suggest that an eye and a half is enough to live.
But actually, unless I misunderstand, even one false eye is enough for White to be definitively alive.
Any White group that manages to make one of these three shapes would be definitively alive:
$$Wcm8
$$ -------------------
$$ | . O . . O . O . . |
$$ | O . . . . O . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . O . . . . . |
$$ | . . O . O . . . . |
$$ | . . . O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -------------------
- Click Here To Show Diagram Code
[go]$$Wcm8
$$ -------------------
$$ | . O . . O . O . . |
$$ | O . . . . O . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ | . . . O . . . . . |
$$ | . . O . O . . . . |
$$ | . . . O . . . . . |
$$ | . . . . . . . . . |
$$ | . . . . . . . . . |
$$ -------------------[/go]
Thus I believe the name "quarter-of-an-eye go" would be more appropriate than "sesqui-eyed go".
This would make it so easy for White to make live groups, and so hard for Black to kill white stones, that I suspect White would be able to play super aggressively and kill all black stones on the board.