One of the easiest things you can do is to take some of your RH licks, and simply try to play them with your LH. It's going to be frustrating at first, but you have to keep reminding yourself how long it took you to get the RH up to its' present level.

I'll often give myself 'mirror' setups to play tunes with. Either with a full band, or on sequences, if I am playing a comp in my LH and brass parts in my right, I'll make a setup with brass in the LH area and the comp sound in the RH. I try to think of myself as having two RH's

For regular full piano parts, then yes, a LH and a RH are the way to go. But as a gigging keyboardist, you are usually called upon to cover a LOT of parts at the same time, and having one hand weaker than the other is a definite drawback. Breaking free from the same 'LH comp, RH solo' habits, and forcing your LH to take on some of the RH's duties can make for a good way to get a practical use for the LH...

Just remember, it's not going to come overnight. But even without a teacher, your RH already knows what to do. Simply work your LH up to mirror it.