kinda depends on the esc themselves.
if they are opto esc, then no problem with the lipo 6s for motivation, and the life 6.6v for rx/servos. could also use a bec with the 6s lipo as well, if you want to not buy a 6.6 life pack, or with another pack of greater than 6v.

and you want everything to share ground.

if the esc are not opto, then, you need to be finding out why their internal bec is not functioning.