Why should Eastern Poland be passed under Ukrainian administration?
Not "Eastern Poland" but the so-called Закерзоння, which some Ukrainians still claim to be their land (remember the lovely FB group "Закерзоння - it is Ukrainian Land"?).
And I already gave you the reason: Ukrainians would be persuaded to give up C, D and L, so that Russia could have her victory and peace could be negotiated, and - in return - they would be granted "their" lands in Poland, within the "union" first, and then when the union breaks up as their legitimate land.
things are slowly picking up
'Slowly' is the keyword here.