Muay thai, american kickboxing, or international rules leg kick (non-thai background)?
From your description it sounds a lil like muay thai...
Things to remember:
stance forward weighted, no more sitting back on your back leg
much more active footwork - you're not going to be rewarded for standing right in front of the guy, get in and get out
close distance with the jab - you no longer have to worry about eating a push kick
head movement - you kinda know this one already
As a southpaw:
shuffle to your right, you want to get on the angle where his lead leg is kind of in the middle of your legs - so you have the angle to throw the hook and the cross.
the hook is only the money punch against a southpaw if you give up that angle and let him get his lead leg outside your's.
The money punch for southpaws (or orthodox against southpaws) is USUALLY the cross coz it's coming at a funky angle - you can even lead off combos with a cross.
learn to parry the other guy's lead hand - if you do it enough, he'll feel like he's only got one tool in the box
Two weapons that should be in any southpaws arsenal are the lead hook to the body and uppercuts with either hand (mainly the rear) - the uppercut is a lot more available in southie vs orthodox fights than ortho vs ortho.
If you give up that angle on your lead leg, counter stuff coming from his lead with hooks to the body & counter stuff coming from his rear with uppercuts to the jaw.
Remember, you're not just backwards - you're different; so anybody trying to get you to just do orthodox stuff backwards probably doesn't know what he's doing.