Steve I'd have probably liked your old Scot, as my dear mother was a Stuart & of a frugal nature & a good work ethic.
I'd best add that the tubes on my Simplex are 1" diameter & I had 1/8" X 3/4" flat strap to re enforce the cut out. It's pretty robust. Also that "cut out" was on the vertical tube between what on the Simplex could be called the seat & tube stay. You have eyes on the area in question & can better determine the modification necessary. If it's to be only a slight cut out might be ok but any cut deeper than 1/4 of the diameter probably not a good idea.
As to the slight bow in the stay, it can be a solid repair & attractive at the same time...they are not mutually exclusive terms. As a fabricator I was taught that the non symetrical yet necessary solutions to a design could be either disguised, hidden or boldly featured. I don't care for the look of full fairings on motorcycles that hide what's going on, left side and right the same. I like the fact that an intake and carb look different than the exhaust system & contrast etc. That's why I favor the early, quirky, artistic look of the first generations of motor vehicles.
If you decide on a bow in the stay make it a fine looking one!
You could also weld a section of tube on the outside of the stay & cut out a clearance notch in the original tube as previously discussed. Then blend the addition and repair into the original stay...no bow just a "trim piece".
Lot of cool ways to get oneself out of a jam with metal just cut, weld, add or subtract till it suits you. Building a new triangle and tank seems a bit harsh & more like "penance" than solution...especially since the tank is so cool, but if you decide to build a new tank. I got dibs on this old one! LOL. Rick C.