My smith has turned down probably a half dozen heavy barrels such as MTU and heavy Palma contours to my specs. Several of these were done because I wanted a sporter weight barrel with a flared end for 5/8-24 threads.
This is a 280 that started as a Remington varmint profile. If you zoom in you can see how the end of barrel flares out.
I've asked a couple gunsmiths if they would do it for the same reasons @83cj-7 pointed out. Get a lighter weight profile but still have a sizeable shoulder for your desired muzzle thread size.
I'm no machinist but it seems like contouring would be easier than fluting. Pricing quoted was pretty close to fluting IIRC. If doing it, i dont see a reason to flute as well. Just have it contoured to hit your desired weight.
Hart Barrels did one for me. It was one of theirs, I don’t know if they will do other manufacturers.
I am not a gunsmith, just an enthusiastic hobbyist with a lot of tools. I’ve done a couple of contours. For me, it was slow and a lot of setup. Managing the chatter was frustrating. I suspect that unless the smith has a CNC turning station, the cost would be prohibitive. You might consider a new barrel, most of them will turn any contour you want.