Most left handed players are used to arcade controls designed for right handed people, and are not going to have a lot of problems with it. Some real trackball games actually used a trackball that was offset to the right.
That's good to hear, I don't want my brother in law having any lame excuses when I kick his butt.

However with a panel that narrow, I would have only done a single player layout but I would have included a second joystick for robotron, etc. The rare times you have a second player you can plug in a gamepad (use the gamepad yourself and let the guests enjoy the good controls).
If I was only making it for myself I definitely would have done like you suggested but all our friends kids love coming over to my house to play the games and they really like to play the two player simultaneous type games like The Simpsons, Double Dragon, TMNT, Metal Slug, Do Donapachi etc. so it has to be a two player panel. The panel still works out fine for me as I can use player two's buttons for Defender and it's joystick for Robotron, Karate, Crazy Climber etc.
Also, it appears you are making the panel much deeper than stock, this might not be the best idea on a lowboy, since reaching for rear controls is a lot harder while sitting.
Yeah the panel is way deeper than stock for this model lowboy, it's original panel would of been 3 and half inches, this one will be twelve inches deep, which is the same as my Gottlieb showcase control panel.

I don't think you guys in the US had lowboys and if you did perhaps they were probably different to the one's we had here in Oz as ours weren't really designed to be played sitting, the control panel height is the same as a normal cabaret cabinet, having said that this proposed control panel will have about 8 and half inches of overhang from the cabinet which means you should be able to get a good part of your lap underneath the control panel on the right size stool which will allow greater reach on the control panel.
In fact just tested it out and it was real comfy, all controls reached easily.