How to fry carnitas

Liver (like any offal) needs to be as fresh as possible. Liver naturally has a dense texture, so over-cooking it results in the dry shoe leather effect that causes most people to hate it.

Soaking it in milk is a common technique, but I grew up with venison liver cooked quickly in a pan with spice mixes (usually a slightly spicy "cajun" or lemon-pepper).

I would suggest looking up some more modern recipes to see if you can find one that appeals to your tastes. Chefs like Hugh Fearnley-Whittingstall, who are keen on re-introducing people to these less popular cuts, tend to have recipes that will appeal to a modern palate.

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.