Cooking through thick liquids

This answer presumes your worry is that by not putting in the pulses/tubers from the beginning, you're actually not ending up with the "correct" result.

My experience with recipes (even from reputable sources) with regard to slow cooked, stewy dishes, with ingredients that take time before they're done, is that they're either short on time, or short on liquids. Either that, or I'm bad with measuring, use ingredients of lesser quality, or suck at cooking (most of the time I suspect the latter two are the guilty parties).

But most likely (and here's the good part), the pulses/tubers are there from the beginning to act not only as a nutritional component, but also serve a dual function as thickener. They're most definitely (IMHO) not there from the beginning to impart flavor to the curry.

So one of the solutions you've already found yourself: Cook the pulses/tubers separately, and add them in the end. The curry will not suffer any loss in flavor. If it's to thin, either squish some of pulses so the starches can thicken it, or reduce a bit longer.

Second solution: Start out with more liquid than the recipe prescribes, and cook/reduce longer, until the desired thickness has been achieved.

It sounds like you are simply making your curry base way too thick. In cooking heat transfers through contact and convection. You use contact when frying things, but when you need a slower cooking process you want convection, where the circulation of the liquids transfers heat from the pan surface through the food. When your base is too thick the heat will not readily circulate away from the pan's surface, and all the heat gets transferred to the food adjacent to the surface, and it burns. You need some more water in there.

I'd avoid blending starches into your curry base, it will make things way too thick and sludgy, and the starches will burn easily and create off flavors. You want to be able to fry off your blended base to get maillard reactions, adding potatoes will not give you the result you want there. If you want to add starch do it once you have fried off your base and added liquid, or if you want a thicker curry then pre-cook the potatoes and add them in at the end.

Here are some tips:

1) Don't make a paste of the onions and tomatoes. Instead keep a ready supply of finely chopped onions, tomatoes, ginger, garlic and green chilies. You can quickly shallow fry these in oil and cumin / mustard a large steel ladle which most Indian kitchens carry . IT looks like this:

Ground onions are difficult to cook - they take too much oil and time and most times will leave a raw acidic flavour in your food. They also cause the viscosity you are referring to unless they are fried in a lot of oil.

2) Buy a stainless steel pressure cooker which can soften your lentils / potatoes / chicken / veggies (brand Hawkins / Prestige). Not only does it quick cook stuff , it also pressurizes the flavour of the curry into your chicken / lentils making it a lot tastier. Please learn how to use it - it can be tricky with water estimation and whistle timing.

Now let's say you wanted to make curried lentils - just pressure cook your lentils with a little salt and turmeric. Then prepare your seasoning with onions, topmatoes, cumin seeds, ginger, garlic and dried red chillies and pour it over your cooked lentils and stir it all together. If you prepare the seasoning in Ghee (unclarified butter) instead of oil, the lentils will taste amazing.

Alternately, you can prepare the seasoning in the pressure cooker, then toss in the soaked lentils, pour water and set your lid to pressure cook all of it - this approach is the best for cooking chicken curry, vegetables like beans and carrots.

Happy to answer follow up questions.