Take all that I have to say with a grain of salt - I'm just a hacker who has tried a lot of defences and has read a lot about chess openings. I don't know if it is a good idea to play both 1.e4 and 1.d4. Your chances to win against a lesser opponent are not diminished if you play 1.d4. I think you have to be at a pretty high level where "drawish" defences mean anything, anyway, and there are plenty of drawish defences to 1.e4 as well. I would say it is best to pick one and stick with it.
The KID is hard to handle but also a lot of fun. Nevertheless, if you think that the French is too much theory, then I would steer clear of the KID.
Speaking of the French, I really don't think that it's as theoretical as you might fear. I play it quite a bit, and most players go for the advance, at least at the lower levels. You will have plenty of opportunity to practice these lines and only need to add something against Nc3 and Nd2 as you encounter them. Many white players are unfamiliar with the subtleties of the French (again, I'm speaking of lower levels), and you can often win a center pawn or take over the initiative relatively easily. In my experience, the French was more direct and gave me better chances to generate counterplay than the Caro Kann (a defence I also like a lot).
Just my two cents,