FYI, if there had been a vacuum leak of any size in the booster, your brake pedal would have become hard, not soft. Anytime the brake pedal becomes soft, it's because fluid is being allowed to slip past a seal, either in the master or a caliper, or, a brake hose from the frame to the caliper could be expanding.
If your idle improved after pumping the brakes, then you need an external vacuum tank. By pumping the brake pedal, that's what you turned the booster into.
Now that your brakes are better, and the pedal isn't going soft, the booster isn't bleeding off the vacuum as often, so the idle should maintain.
In other words, your total problem was the master cylinder, however, and additional vacuum tank would have taken care of the idle problem until you replaced the master.
Take care,
~Chris