There are two different Weber 32/36 carbs, the DFEV and DGEV, which are laid out as mirror-images of each other. If your carb is mounted with the fuel line fittings and float bowl towards the rear, that could explain the stumbling/stalling issue on braking that you described.

The DFEV is rarer to find and thus usually more expensive, but it's simple to mount with the float bowl in front and stock throttle cable routing coming at the carb from the exhaust side of the engine bay.

The DGEV and is easier and cheaper to obtain and can be mounted with the float bowl in front, but this orientation requires some tinkering to re-route the throttle cable to come at the carb from the intake side of the exhaust bay.