How can pre-main sequence stars radiate more energy than main-sequence stars? How can a pre-main sequence star radiate more energy by gravitational contraction than a main-sequence star can by hydrogen fusion?
Although pre-main sequence stars have lower temperature, they are essentially huge clouds of gas, often as large as 1 pc wide. The luminousity being proportional to square of the radius is essentially large for pre-main sequence stars.

Plus, the problem with gravitational contraction is not the amount of energy that can be generated per second. That can actually be larger than that produced from fusion if you insist on really massive objects. The logic, when we ruled out gravitational contraction as a source of energy for Sun, was that gravitational contraction cannot sustain it for long. Geologists knew from their dating science that Sun had to be older than grav. contraction accounts for.

Thus, admit it. Gravitational contraction makes pre-main sequence stars radiate more energy than main sequence starts, but that's just luminousity and not really energy.
Luminousity is energy per second.