From the lack of detail in your question I'm going to assume you don't have a tensiometer. If you do, please tell us what tension you're actually using and what the limits for your rim are.
edit The "final half turn" is, as Andy points out in the comments, scary. That will give you an extra 100-200N of tension at a time when you should be working in selective 1/4 turns (ie, some spokes get tightened 1/4 turn, others get loosened 1/4 turn) or even smaller increments. It's also something that will stretch spokes (ie, they'll tighten beyond their elastic limit and become permanently deformed). You can't undo that, you have to replace the spoke as it's permanently weaker than it should be. And it's not necessarily the spoke you were turning when the problem became obvious that has stretched. A spoke giving like this will produce the minor taco problem you talk about.
Building wheels without the proper tools is hard, and you have to expect to make a lot of mistakes. Completely redoing an old wheel is harder because you have spokes that are bent and some may have deformed as well as dirty threads and nipples that may be partly seized in the rim. Much online advice says "it's easy" but is specific to small wobbles recently appearing in a reasonably new wheel. You're well past that now.
What you're trying to achieve is perfectly even tension on each side of a straight rim. To do that you either need to measure the tension or do extra work to make guessing the tension easier. There are various approaches and I'll make suggestions for each:
nipple feel. You guess the tension based on how hard it is to twist the spoke tool/nipple. For this to work you need to have clean threads and clean, even seating of the nipples in the rim. Very unlikely to work on older rims without eyelets unless you take the wheels apart and clean the nipples before oiling them and reinstalling. You can fake this to some extent using a degreaser and penetrating oil but if you also have rim brakes cleaning up afterwards is both crucial and difficult (you'll need to use a light solvent to remove the oil).
Using this method your problems above may well be caused by one or two sticky nipples that feel tight in the rim, meaning the spoke is looser than you think it is.
Spoke pinging/musical method. This can actually work, but relies on the length of the spoke section you're pinging being the same for all spokes on one side, and your sense of pitch being accurate. IME I can get a 1-2% variation by stress relieving a wheel, and 5% by pushing spokes back and forth. But I have perfect pitch so I'm excessively sensitive to changes like that. I have seen someone build a wheel this way and get nice even spoke tension. It was ~10% off the tension they wanted, but it was even and the wheel worked fine for years afterwards. Using this method your problem is that you're not getting the pitch as accurate as you need. Maybe go round and push all the spokes the same way then ping again.
Position is all. Don't worry about spoke tension, just get the rim straight. This can work, much as buying a lottery ticket can make you rich. It's just that unless you happen to have even tension when the wheel is straight it's going to go out of straight very quickly. By iteratively straightening and stress relieving you can eventually get a wheel that will stay straight for a while. The more you iterate the longer it will stay straight, as long as you keep refining how you define straight. People doing this often talk about needing to get wheels straight to better than 0.1mm. Using this method your problem is that you're missing half the picture, spoke tension is also important.
These days a Park Tensiometer (TM-1) costs about the same as the labour for two wheelbuilds. I suggest making a truing stand out of an old front fork and buying the tensiometer rather than buying a truing stand and not having a tensiometer, if you're looking at spending money.
This question is more encouraging about the pitch method and is worth a look.
