I still don’t think this has been explained adequately.
First you will need to open up your joystick so that you can see the clear plastic restrictor. This is also called a gate. It is the circular part on the bottom of the joystick with a square hole in it.
It has four plastic clips going through it. You will need to bend those back a little bit until you can slide the restrictor off. Now you can see the switches that are used to activate the directional inputs. The are soldered to a small pcb and there is a white connector on the pcb. Temporarily unplug the connector.
Now you will need to pull off the PCB with the switches on it and rotate it 180 degrees. This will reverse all directions on the stick so now up is down, down is up, left is right, right is left.
Reconnect the white connector and put the restrictor back on. Now you will need to swap the quick disconnects on the buttons so that when you turn the stick around punches will be on top and kicks will be on bottom. You said you know how to do that so I think you will be ok.
As a side note there are actually many players who use a joystick on the right hand side. In Mexico and South America this is the standard on arcade machines. They have gotten so used to it that when they come to the US to play or use an arcade stick they play cross-handed.
Of course there’s Clothhand AKA Seth Killian. I asked him about this once and he said he started doing this back when he played Defender as a kid.