I hope I'm answering the right question. Your title says "grainy" but then the rest of the question talks about "gloopy". If the problem really is grainy, I think the issue may be that you are using better cheese than in the past. Well aged cheeses tend to get a little bit drier and crystalline, and then they don't seem to melt as well. I've had grainy in that case too. Sometimes I'm happy to live with a little bit of the graininess to get the better flavor.
First, I don't know where you people all get these gelatin-filled Turkish delight recipes. Turkish delight is made with starch, not gelatin (at least the recipes used in Turkey are all with refined starch or rice flour). What you are making here is jell-o (if you use small amounts of gelatin) or gummi bears (if you use lots of gelatin).
Second, about the taste. It is normal that fresh apple juice loses its taste when it is cooked. The normal Turkish delight tastes of sugar. Its aroma comes from strong aromas added to the liquid (rose essence, or artificial aroma). You don't preserve natural fruit tastes in Turkish delight. Even if you wanted to, I don't think there is a way to do it with apple juice. Some stronger tasting fruits (cherries, raspberries) could give a syrup with more taste, but are not part of traditional lokum.
Third, about the temperature. Your observation is correct, you are just evaporating the liquid. In some cases, it might be desirable to start with more liquid and evaporate, so you get more concentrated aroma - for example, if you have started with pure rose water. But if you are making a recipe which requires concentrated sugar syrup, it is OK to start with a ratio which creates saturated syrup at room temperature (3 parts sugar to 2 parts water) and cook until the desired consistency is reached (this is recognizable from the boiling point).
For most recipes however, you don't want a concentrated syrup. The candy hardness is defined by the amount of starch used. In this case, you just mix everything and you are ready after it has bubbled, just like any pudding. The amount of sugar seems to be 1 part sugar to 2 parts water.
Best Answer
I put the pan with the milk inside a larger pan containing some water. This makes it much harder for the milk to boil; but it doesn't need to boil in order to turn for cottage cheese. It takes much longer to turn this way (1-2 hours), but during that time I can pretty much leave it alone and just check back every 5-10 minutes to see if it's started to turn yet and give it a quick stir to break up the skin.