If I ever owned and SBR or SBS, yes I would notify the ATF that you've reconfigured the gun into non NFA territory. I would sell the upper or the barrel though and include a proof of sale, unless the upper/barrel is what's considered NFA regulated. Idk, I've always thought that it was the lower/frame that had the serial number.
From all I've read, I think I'm never going to SBR anything and will just pay the hefty sum for a Sig brace or adjustable Sig brace and put that money towards a company and workers that actually adds value and creates something in the world instead of gov't that exists solely to redistribute wealth through draconian tactics via taxes.
There's only two pistols I want to Sig brace and shoulder fire and that's a Ruger Charger .22 and a 9mm with a 9 or 10 inch threaded barrel. Can do it with the Charger now, but that particular 9mm I'll have to wait on. Hopefully Ruger comes out with a pistol variant of their new PC carbine.
From what others on TFL have said, the SBR/SBS novelty wears off quickly... probably much more so now that the pistol brace exists.
So, as pertains to the OP's question, I wouldn't SBR anything. Do as much as you can now with a Sig brace as I don't think a higher cheek weld recontructs the brace to be fired from the shoulder. Before the ATF said it's okay to shoot them shouldered, there was a tactic to "cheek fire" them in which the brace never touched the shoulder, which at that time was legally making it an SBR.
I wouldn't put anything on the rear portion of the brace though, because that's where the shoulder touches it. That could be construed to be making it into an SBR.