I agree with the others - I started out using a double-pot method, but found that I get pretty much the exact same results using direct heat, with less muss and fuss. A key is to have a really good pot - I would not recommend that anybody try direct heat using a cheese pot with a thin stainless steel bottom, for example. But if the pot has, for example, a large "pad" of aluminum wrapped in stainless on the bottom, that will help to even out the heat pulses.
That said, there are two things that give me a little bit of concern in your post. One is when you say that you may get a tiny bit of milk stuck on the bottom - that does suggest that you are getting some localized over-heating. For comparison, in making 60-70 cheeses using direct heat, I have never gotten any milk stuck on the bottom. That may be a difference in the stove, or in the pot, or in the heat setting ... ??
The other thing that gives me pause is when you say that you use direct heat to maintain the temperature of the curds. As Gregore has said, I would strongly recommend against applying any heat throughout the curd stage until after the curds have been cut. The thermal mass of even 2 gallons of milk is pretty significant, so unless you are making cheese outside in the winter, you should not drop more than a degree or two during the curd formation, and this will not affect the results negatively. However, adding heat can disrupt or weaken the action of the rennet.
Basically, I would suggest that heat should only be applied at times when you are able to stir the liquid regularly - so during the ripening phase, I also turn the heat off; again, at most it will drop a degree or two, and I can easily raise it back to the target temp before adding rennet - but often the temp has not dropped enough to need to do even that.