I had this same problem, but think I've found a workable solution.
I have a Saitek ST220 handle hacked onto a Happ Ultimate that was doing the zig-zag thing really bad as originally installed.
What I did to fix it was cut a piece of wooden flag pole (1" diameter) the same thickness as the factory "square" actuator and bore a 5/16" hole through the center of it.
This gives very positive contact to the 4-way positions; but still allows it to contact both switches for 8-way operation.
I didn't do any other modifications to the switches or anything, and the problem appears to be solved--at least for me.
I think the problem with the Happ Supers is that they have those metal levers on them.
(The levers do make them feel better, and more sensitive, to me for most games however).
The levers on the Super allow the actuator to trigger the diagonals easier than the bare switch buttons on the Ultimate, resulting in the zig-zags as described above.
My only complaint regarding the stick I put together is that I'd like a little heavier return spring on it.
With the larger handle, it is a little soft, but plays REALLY well for me.
I'll keep working on that, and post here if I run into anything worth posting.
I was originally planning to get one of the Happ Heavy-Duty trigger sticks, but decided to do this hack until I get the money for it.
If this works, I may stick with it; and build a few others into some of my other control panels.
The ST220 has three thumb buttons in addition to the trigger, and I think I got the one I just used for about $10 on sale.
Couple that with a Happ Ultimate for about $15, and I can build 4 of them for the price of 1 of the Heavy Duty sticks.