Nice 90s vibe. Web target is cool. The invaders demo though... I have to say AD+W is not a good set of key bindings for that game.
Pressing forwards to shoot feels wrong though.
This feels like it would be better with double keybinds. Arrows + Space for non-gamers, WASD + space for gamers.
Don't just change it to arrows though, that's going to be painful for laptop users who don't have those crappy half sized arrow keys (see macbook, framework, etc...).
ZXCV(ASDF)+arrows I would say is more standard for non-mouse games with keyboard bindings, cave story and touhou both go this route.
I searched and found some left-handed keyboards, but they are missing important things. Like they use qwerty-layout instead of ][poiu. The worse, they keep Enter on the right side and CAPS on the left. So you cannot remap Control key onto CAPS and use it with your pinky without twisting your right hand uncomfortably, when your left hand is on the mouse.
Maybe for first-person shooters, but not for shmups, and definitely not for classic arcade style games.
To your second point the reason it feels unnatural is because mapping movement + actions to a single hand is usually not a good idea if you have the opportunity to distribute them.