Cheap joysticks will generally cost more money and time to mod them to make them better than it would buying a gently-used Hori HRAP joystick or Mad Catz TE… The Hori and Mad Catz joysticks are the most reliable mass-production Asian joysticks on market. With everything else you’re pretty much taking a chance on PCB failure in the near-future. That’s the general case more often than not with grey market product.
“Cheap” and triple-compatible joysticks are an oxymoron. Triple-compatible joysticks start at $150 if you want any level of quality. The PCB’s on these are still a dicey proposition with higher levels of failure than the licensed product.
You just aren’t going to a quality joystick for much less than $150 that supports PS3/360/PC compatibility out of the box. If you can find a used Qanba Joystick – very rare since the main reason for their popular is triple compatibility --, then maybe you’d be able to get it for $110-$120 used. The Qanba does use Sanwa parts. Qanba’s have also been manufactured with Seimitsu parts installed, too.
The $55 joysticks that do support triple-compatibility are not the best quality and generally have to be ordered from overseas which can jack up the price up to at least $80 with shipping unless a domestic vendor has the joystick in stock. Again, you really wouldn’t be saving anything buying and gutting a joystick like that to install higher-quality parts. No guarantees that Japanese parts would fit into a Mayflash/Paewang joystick, either… they’re Korean cases and those generally are not made to mount Japanese parts without serious modifications… They also don’t generally have the best reputations to begin with, either…