I apologize if the title of this topic is a bit odd, but I'm not sure what you'd call this technique.
I'm a self-taught guitarist who has branched out, in the last year or so, to piano. I've brought a lot of my guitar technique (a learn it by ear, make-it-up-as-i-go-along style of playing, inability to sightread, etc.) to the piano. I have a very specific style in mind for what I want to do on the instrument; basically, it's the Ray Manzarak (of The Doors) style of playing, where he plays the (relatively) simple bass lines of the song with his left hand on a Rhodes keyboard bass and chords or improvisations with his right hand on a regular keyboard or organ. I'm able to do both the bass parts and the improvisation (again, coming from the guitar it's nothing too fancy, just major, minor pentatonic scales that I know from playing the guitar), but the problem is that I can't do them at the same time.

I've been learning some simpler piano tunes by ear, to try and get the feel for playing with both hands at once. To give you an idea, i can play play some not-too-difficult pieces like "Greensleeves", "Moonlight Sonata" (the slow bits, anyway), as well as that kind of strumming emulation you hear in Beatles tunes. The bass lines that I'd like to play, as I said, are usually pretty simple; in the solo section of 'Light my Fire' he's basically playing the major notes of Am and Bm chords, and I thought it would just be a matter of knowing the lines so well i could play them without thinking, but that hasn't really panned out the way I'd hoped.

I suppose what I'm asking is this: are there any exercises specifically designed to get my hands playing two different things at once? I don't need to have incredible technique or any sort of super advanced skills, since my only real goal right now is to play this way.
A few side notes:
I've found some recordings of Hanon's exercises that I've transcribed and have been practicing for the past few weeks. I felt that they were helping me tremendously, but since I've found this website I've heard some very nasty criticisms about them, so I'm not sure if i should continue to use them or not.
I also know that most of my problems could be solved by finding a teacher, but I don't really have the time or money for one at this point, unfortunately. Someday when I've finished school and am settled in my career I'll take some lessons and maybe become a proper musician, but for now I'd just like to be satisfied with my improvs

Again, my apologies if this is the wrong place to post this kind of topic, from my short time on this board this site seems like it is mostly dedicated to classical music, but there seem to be so many knowledgeable and helpful people here.
