When I set the tensions on my older machines I use Size 50 thread. I have several Singers and other brands that actually state in the manual to use that size thread when adjusting the tension. The thread I use is not the new stuff, but the old stuff from when the machines were made. There is a difference. It's my experiance that once the tensions are set with the old Size 50 thread, my machines are much less picky with the modern stuff.
On the ZZ machines that skip stitches on only one side I've usually found the needle is not centered in the needle slot on SS so when on ZZ the swing is more to one side than to the other. When centered the skipping is greatly reduced or eliminated. I've got a couple I had to do that with.
I also always use a thick material such as denim or at least a double layer. Seriously, how often do we really sew single layers of fabric? Almost never when making things. Even when I do a pattern test on my ZZ or cam machines I use a double layer or a thick fabric. It's my thinking that with one layer of normal cotton or similar, the needle drops down just a teensy bit too far and doesn't always catch the thread on the way back up.
Joe