In my opinion, the mounting to the door as you describe is entirely over the top in terms of strength. Your box mount would be stronger than the hinges holding the door onto the van (or close to that) with ten bolts and a 1/4" steel backer plate. That's not a problem in itself, I guess, but it is unnecessary weight. Likewise, I suspect that 3/16" aluminum is very much overkill for the weight that will be carried.
Per the US DOT, as I understand things, carrying propane (at least in any sort of permanent configuration) is illegal if the propane tank is either above the roof, below the vehicle frame, or extends out beyond the front or back bumper. That possibly might not apply to a portable tank in a cargo box, at least technically, but that does nothing to address the rather obvious safety concerns that led to the regulations. In a crash you would prefer not to have the propane tank obliterated and its contents released suddenly. There are also requirements for venting a compartment carrying propane tanks (the bottom needs to be vented to the outside). I don't know anything about what Canadian regulations are like.
Would the hose you referred to be a propane connection leading through the door? Are you not going to install your permanently mounted tank for some reason, or is there some other reason to need another tank connected?
About the only other suggestion I would have is to make sure the box doesn't block the lights. In particular, it looks to me like it would obscure the left turn signal for anybody who is much to the right of the centerline of the vehicle. Angling the end of the box inwards would help there, I think.
By the way, your English is excellent.