One thing you may want to take a look at is the significant distance from the brake pedal actuation arm to the actual heim joint for the master. A distance of ~25mm is certain to cause at least some flex of the pedal actuator arm. Unfortunately there is little you can do about that.
An increase of master cylinder piston diameter from 12.7mm (1/2 inch) to 15.875mm (5/8 inch) would decrease the overall ratio by 56%, meaning you would have to literally put all your weight on the pedal to get any significant braking. Not good. At least the pedal would be nice and firm.
A 14mm master would decrease the ratio by 21.5%, better, but effort would be that percentage greater. That is if it will bolt up without major modification to the rearset.
For reference I checked my rear brake, which I rarely use, and found that the movement of the pedal before any discernible braking occurs is around 15mm, and lockup maybe another 10mm. If yours is significantly greater I'd suspect either the Sato rearset brake pedal is dimensionally different that the stocker. Unlikely, but possible. Or there is an air bubble at the high point of the system, which is the banjo fitting on the master cylinder that no amount of "pump up, hold, crack the bleed screw, close, repeat" will address due to the small amount of fluid moving. Perhaps a banjo bolt with an integrated bleed fitting would be beneficial, but there is an alternative: remove the clevis pin, unbolt the master cylinder and the reservoir, pivot the whole assembly up until the reservoir hose is the high point, then retract the caliper piston. This will force any air out of the banjo fitting and into the reservoir. That is one of the reasons why I always use AN fittings instead of banjos: bleeding is much easier due to no convolutions in the fluid path.
One more thing you can do is fettling the master cylinder. Stock, the rear primary piston seal at rest position is at least a millimeter or more from the compensating port, meaning the first 5 to 8mm of pedal travel is used to simply cover the port to begin pressurizing the system. Normally when I am building a master I position the primary seal to occlude about 10% of the port using thin shim washers. Pressurization starts almost immediately. It's not easy, but worth it when on the track, and in my case on the street.
And of course there is the Brembo thumb brake setup mentioned by LDH. Undoubtedly a perfectly functional solution, but at a retail price of $2000.00 it's also a perfectly unreachable solution for the average street rider. Now if you got one free for "testing purposes" it'd be a good way to go. That is if it can be mounted to the bar instead of the fork.
My mistake: the Sato thumb brake is listed at $650. At one third the price of the Brembo it's still ... pretty expensive.
Rob