I'm a big curry aficionado and am trying to cook curries that both taste good and require minimal preparation during the week. I like to make both vegetarian (usually, green/red lentils, fresh) and chicken-based curries.  For that reason, I'm starting by blending the masalas, tomatoes, onions, etc, in a blender, frying, adding the rest of the ingredients, adding water, and then reducing until finished.  I've noticed that both the tubers and the lentils cook very slowly using this method.  If the blended mix is particularly thick (e.g., it includes the tubers themselves or ground nuts), I've found that it hardly cooks at all.  I've figured that the problem has to do with the viscosity of the cooking medium (starches obviously make it the most 'gluggy') and feel that things would work much better if I cooked the lentils in water and then transferred, once cooked, into the sauce, but the recipes I've read all use the all-in-one method that I'm following without much success.  In addition to not cooking, things seem to require very frequent stirring and sticking is a big problem.  Is there any solution to this? 
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.  