Just in case, is it just something that dripped into the oven? Unless you've baked something else since you started having problems with the chicken, just preheat it and see if there's any smoke. (Or inspect the bottom, but you might miss something.) If there's any smoke heating an empty oven, then you need to clean it.
Assuming that's not it, most likely it's still the olive oil. Depending on the oil, some of it will indeed smoke at 350F, and on top of that, it's possible that your oven is actually hotter than it thinks. Unless you've checked the temperature with a thermometer, it's quite possible the temperature is 25-50 degrees higher than it claims, especially if it's old. You could try lowering the temperature further.
But really, there's not really much point cooking this with extra virgin olive oil. It loses its flavor when you heat it to those temperatures, even if it doesn't smoke. You'd be better off just using a neutral oil (vegetable oil or whatever you prefer), and if you want olive oil flavor, add a bit after you're done baking. You probably don't actually need very much oil when baking, so you could reduce the oil there, and make up for it with olive oil at the end.
Paneer butter masala, malai kofta gravy and matar paneer are part of the North Indian cuisine where the base is mostly the same with some minor variations (like excluding cumin seeds).
So essentially, you have a common base gravy for sweeter dishes like these and then you have a spicier gravy for other dishes.
Many Indian cuisines have this pattern. For example, Gujarati cuisine will have red chili powder, turmeric, garlic-ginger, mustard seeds, cumin powder, fenugreek, cilantro and jaggery, etc. as a general base with some additions and subtractions of the vegetable ingredients.
Similarly, you'll be able to find common base gravies across Indian recipes and cuisines.
But, when you say:
"In addition - It seems to me that the same thing could be said about aloo gobi, chana masala, baingan bharta, and many other dishes - Basically the same frying of onions, ginger garlic paste and tomatoes, but with a different ingredient added at the end (for example eggplant for baingan bharta)."
You are making a generalization which is not necessarily true. These recipes can vary quite a bit based on regional tastes, specially baingan ka bharta. This dish is a signature dish and needs a seasoned hand to deliver it right.
So, you are right when you say there is a common pattern across recipes.
But certain dishes like aloo gobi will exist in different forms across the country. But rest assured malai kofta, paneer butter masala and matar paneer are only prepared in the North Indian style.
Best Answer
With Olive oils, the more refined they are, the higher their burning point. So you are correct, an Organic Extra Virgin Olive Oil would be a terrible choice for Indian cooking (would cause effect on taste, smell, and nutrition) which has prolonged periods of sauteing on high heat.
Lower quality olive oils, or a light olive oil, interestingly, would be a better choice. They are much more refined like vegetable oils, so have a higher burning point. But at that point, you'd consider why are you using Olive oil?
Consider using refined butter (ghee) or coconut oil for Indian cooking. Ghee and Coconut oil will rarely smoke or burn and can stand high heat pretty well. I believe traditional Indian cooking uses ghee.