Another disciple! I'm gonna be rich!
You might -- could perhaps, maybe -- discover that the 110 V welder is inadequate. My friend Peter tried using his on Millicent, and got nothing but chicken scratchings. (I used a 220 V stick welder.)
I'm old and got dizzy trying to study your fancy drawings and detailed ideas, so I will generalize:
An experienced fabricator might jump right in with the 1" insert and pinch down the "hat section" and weld it up. But before you do it that way, make sure you fully understand how you are going to line everything up, and where you will be welding -- including inside the hat section on the hidden top and bottom of the inserts. A long overlap is probably more important than a perfect fit.
I added shims the full length of my inserts simply because it was the easiest way to get perfect alignment. In retrospect, I wasted a lot of shim material, because I could have accomplished almost the same with a short shim at each end. By almost the same, I mean the same fit, with only a tiny loss in strength.
Keep in mind that most of the strength in a structure like this is in the outer dimension of the piece, and not in the wall thickness. (See "long overlap" above.)
So... using only one 1" piece for the insert, would lose you a ton of sideways strength. I think I used 1" x 1 1/2" rectangular tubing, (plus shims), and that 1 1/2 is the big strength that will help keep the roof on top if the bus tips over, compared with just 1". Apparently, you understand that. Good.
Do you mean that you would slice some 1" square tube to 3/4" and add to a 1" for a full 1 3/4" insert? That would be terriffic. My only worry would be all that "ripping".
How about using two full pieces, for a 2" insert? Right.... The skin wouldn't fit.
I like the 1 3/4 idea, and then I wouldn't worry about the slight gap on the side. Clamp the insert into one corner of the hat section, and weld everything you can reach. Then pinch the third side in and weld that. Or stick short flat shims in there for neatness.
You may have noticed that I put some diagonals in Millicent. You might want to do that too, since you are going up so far.
And you know to build and use sturdy lifting guides, right?
Get to work!