Your making life much harder and expensive than it needs to be with all those rib plates.!!. .

Two large thick walled pieces of box section arranged in a L shape with a few triangle braces at the rear will easily match your gantry in strength and be much cheaper and simpler to achive. It will be much easier to achive accurecy as well because with that thickness of steel on those square tubes then heat from welding will almost certainly have an affect either pushing or pulling on the boxsection with so many braces to weld, even on just 2 sides.
If you used a Tig welder you may have chance but even then I'd be surprised if it doesn't.! You will certainly have to take it very very slow keeping welds short and leaving plenty of time between to stand any chance.

Your design will be strong but no stronger than more conventional setup and 3 times harder to achive and probably 3 times more expensive.?

Also Please don't tell me this is just for cutting wood with occasional aluminium use.?. . . .