Wow, great question!
I pick the yarn while knitting, using the tip of the right needle to do all the work; while purling I use my left index to pull the yarn down behind the tip of the righthand needle (but in front of the lefthand needle of course) and then pick the yarn with the right needle again to pull it back through and off the left needle.
I taught myself from the book "Knitting in Plain English" by Mary Rigetti (not sure about her last name). Watching Amy's videos on how to do various things, I think I knit/purl using the same movements she does.
I think it would make things more efficient in the long run, so it would be worth it to give it a shot. If you find it's too miserable you can always go back to your t-n-t method! I like that I don't have to work so hard to get a stitch, lol. Then again a lot of english style knitters knit a whole
lot speedier than me