Here let me start from the top I will document all the things it could be and all the things that it may be.
If the vehicle when braking is shaking and the wheel shakes then the issue is in the front end. Start by checking the rotors, even though they are new out of the box them may need to be resurfaced. Also check the calipers to make sure one is not binding and causing the vibration. Second check all the ball joints and bushing in the front end if one is loose this will cause the shake through the front end and steering wheel.
If the vehicle is shaking and you feel it in the pedal or on the seat and rear of the vehicle then the drums may need to be resurfaced. Have them check all the hardware and make sure that all the drum system is in working order. This may be a stretch but since you have tried everything look over the differential make sure any bushings and the rear suspension are all tight and nothing has play.
If the entire vehicle shakes then you may have a torque converter issue. Even though it was checked previously may want to try the check provided above. What happens is that the torque converter when braking will still be cranking away and causing the entire vehicle to shake. When you make it shake kick it into neutral if the vehicle stops shaking then that will condemn the torque converter.
The booster can only be checked using a vacumn pump, you pull a vacumn and it should hold. Also check the hose to make sure that it is not dry rotted. The valve should be on the side of the side of the booster and should have a huge vacumn line to it.
Other than that the only thing you can do is recheck the mounts and all the items previously checked something had to have been missed. You stated that the carburetor need to be addressed it may also be contributing to the issue but it is highly unlikely it would make the vehicle stall.
If I answered your question please click ACCEPT. I do not get paid until you do even if a deposit is made. Any Tip/Bonus/feed back is always welcome