Nope. NEC does not mention transformer loading.
All NEC covers is transformer overcurrent protection -- there, you're allowed to go to 25% over transformer rating. So the max you could possibly overload your transformer would be 25% (assuming you're running close to nominal voltage).
Your 3-5% overload doesn't bother me one bit. The worst you'd do is knock a couple years off the transformer's expected life.
Note that utilities, who are not held to NEC, will commonly load transformers to 25, 40, even 100% over their nameplate rating. Of course, they don't mind replacing them a bit more frequently than we normally would. Matter of fact, this works out to be cost effective for them as it helps keep them from oversizing transformers (that's why they do it!). Most customer-owned transformers are only loaded to about 30-50% of their rating -- that's negligable extra cost for a customer, but that kind of overcapacity would be super expensive for a utility.