Definitely go with that higher amperage "brick". That'll push the uZeus up to 2000mA on the +12 rail.
The problem you're running into is "inrush loading". When you switch on any electronic device, there's always some sort of higher load for the first few milliseconds, and that can pop the supply if you've gotten the current spec too close to the quoted operating tolerances. To avoid this, don't let each summed current value on the build's DC rails exceed 3/4ths of the stated P/S's maximum current per rail. This is actually a pretty common rule of thumb with modulars, tbh.
As for consumption specs, the reason you don't see this inrush figure is that sometimes it's an important factor, and sometimes not. As you've noticed, yep, digital modules are notorious for inrush issues. With simple analog modules, not so much. So everyone pretty much agrees that the "normal load" current figure is the correct thing to cite, and you just keep that "3/4ths rule" and the total current per rail in mind during the build process as that ceiling can vary from module to module and P/S to P/S.