Welcome Nick!
Being fairly new here myself, I can't say with absolute certainty what the minimum thickness for a firebox should be. What little experience I've had says that you need AT LEAST 3/16". Any thinner and enough air flow could create enough of a hot spot to warp the firebox or burn through.
The only time I think you can get away with 1/8" is if you're using propane burners only or have a suspended basket for coals.
Most of the guys seem to be using 1/4" or 3/8" plate on the square fireboxes for the sake of longevity.
Save that 1/8" though. I made mine out of 1/4", insulated and skinned it in 1/8"
There's no sign of any warpage, and I've had that firebox full of oak splits and the air opened all the way up.
Sounds like you've got the hinges figured out. I've seen guys use weldable pre-fab "bullet" hinges, fabricate their own and cut sections of heavy strap hinge(this is what I did) all with equal success.
Rule of thumb: If it's still holding the door on when everything's glowing red, you're GOLDEN!