What can be used safely (e.g. basalt “hot stones”) to fill volume of shallow pan for deep frying

I think that your problem doesn't come from using the wrong cut, but from using the wrong quality tier of meat.

The cheapest pork in the supermarket, no matter which cut, is produced from cheap mass-held pigs with a certain type of "lifestyle" - no movement opportunities, cheap feed, lots of antibiotica. It produces a certain kind of meat, known as PSE meat, which stands for "pale, soft, exudative". The last word means exactly what you describe: a meat which loses lots of water during cooking. So no, you cannot get more "bang for the buck" by changing the cut.

I still assume that you are getting a better price per gram cooked meat from buying cheap meat and cooking it down than from buying expensive meat which will lose less water, so I guess that, if price is the most important part for you, you shouldn't change anything.

Another word about quality: the S in PSE is also your enemy when making goulash. Generally, you want lots of collagen in goulash, and some fat for taste. PSE meat has almost none of them. The old idea that cheap meat is best for goulash comes from times where the difference in meat prices was based on the cut: a shoulder cost less than a filet, and that was it. Nowadays, this connection still holds for the same animal, but if you look at the different price tiers, the cheapest meat, especially in pork, is not at well suited for long and slow cooking methods. If you buy cheap meat, the best you can do with it is usually mini-steaks or schnitzel, heavily dressed to make up for the lack of taste.

You shouldn't heat a non stick pan without the oil, because it is too easy to overheat it and ruin the coating.

So, I put oil inside first, and tell by the state of the oil. It smells, looks and flows different when it is hot enough. You can also learn to judge if there is sufficient heat when you hold your palm at a given distance above the pan, but in my experience, you learn to judge by the oil before you have gotten good enough to keep the same distance and to distinguish "enough" from "not enough" heat.

If you don't have enough experience to know when the oil is ready, you have to do it repeatedly until you learn it. It takes a few less-than-great meals if you do it purely by trial and error, and goes better if you use an infrared thermometer. You can also try floating cubes of stale white bread and watch their browning behavior, but I find this method too involved logistically - you have to have the bread, cut it, then deal with messy pieces of oily bread, and end up with slowly charring crumbles in your pan.