Transformers are traditionally undersized due to a diversity factor. You may have all the items you listed, but how many are running simultaneously?
As noted above, their rating is for continuous duty...temporary overloads are factored into the equation. Unless they remain on for extended periods of time (causing the transformer to overheat), they won't hurt a thing.
We fuse our transformers for 100% overload. So assuming a 7200 volt primary, we would stick in a 5 amp fuse (it calculates out to something like a 4.16 fuse, but that is not a standard size).
That would get you up to 36 Kva (150 amps on your side) before the fuse "theoretically" should start to melt.
But primary fuses like the standard S&C fuses we use don't actually start to open (referred to as "minimum melt") until they hit approximately twice their rating. So the 5 amp fuse mentioned above won't start to melt until it approaches 10 amps (which doubles the Kva again).
So pulling 125 amps intermittently won't hurt a thing, unless you leave it on forever. But be cognizant of the possibilities, and check with your POCO if you're worried.
[This message has been edited by WFO (edited 12-23-2005).]