For the most part I agree with some stuff that has already been mentioned, but I'll add my two cents as well.
I don't think the Byakugan should be constantly active. In the manga, nobody has it active 24/7 so it makes sense that in SL it would have a limited amount of turns. I do think though that the amount of turns should last longer and increase as the resets stack, as previously suggested by Ratatosk, because the more experienced you get with the Byakugan it makes sense that you would be able to sustain it for longer. It would be nice if Kaiten got a power boost as well. Leave the chakra costs as is.
If anything, in the past Neji has been more inclined to make it more difficult instead of beefing up KG because otherwise everyone would be breezing through resets. There's always the option to leave Byakugan as is and just nerf Sharingan further XD
Regardless, Neji already has his hands full with the KG swap and other secret stuff, and he's already been nice enough to do a revamp before so this kind of request is more on the backburner if anything.