Since you will have 2" of overlap on each end, you will want to make sure every edge is welded. You welds will be a more secure than butt-end welding the tubes to the hat channel. The further out you can put the welds (i.e. the longer they are) the less severe the loads are on the welds.
To help you decide what to do, I prepared a little thought experiment.
For a visual, I took a piece of hat channel (steel black) and put in a piece of square tubing (blue). Well, actually it is angle iron that looks like square tubing. I placed a tape measure on the blue metal, so it is a bit difficult to see. However, I think you get the idea.
Here is what a 2" overlap looks like:
20200422_011510 2 inch overlap.jpg
Here is what a 4" overlap looks like:
20200422_011429 4 inch overlap.jpg
Of course, you will be putting an outer skin on and attaching it to the hat channel, same for some sort of inner wall. All of this adds strength to the overall structure. Bear in mind that since you plan on raising under the windows, there will more weight and thus more stress on the structure you are building to hold up the roof and windows.