Conflicting info on levelling with stabilizing jacks or not.

Absolutely nothing conflicting about this...they are for exactly what they are called..stabilizing jacks - not leveling jacks.
They are not designed to lift/level and neither is the frame of you trailer.

For side to side, drive up on (shims) as you call them, or get your self a set of very handy, lightweight, easy to store and easy to use Lynx Levelers.