It will exceed the current rating on the power transformer. Look at the RMS transformer current; maximum is 3.5 amps RMS, and a DC supply will exceed that significantly. Since dissipation goes as current squared, even a small excess can drive internal temperatures too high for the materials. Shorts inside the transformer are a serious safety hazard, since the high voltage windings can short to something grounded. It's unsafe, don't do it!
The same transformer is used in the SEX, and is just barely capable of heating a pair of 6EM7s (total 2.1 amps DC). At 2.8 amps you will generate nearly twice the heat in that winding - enough to melt the insulation on the wire. DON'T DO IT!!
It also exceeds the average current rating of the diode, which is 1.0 amps (2.0 for a bridge, since each diode conducts half the time). They will just blow up, possibly shorting out and blowing the fuse. Tiny shrapnel is the main hazard there.
Best bet is what people did with the old original Foreplay - buy a separate wall-wart power supply rated for 6 volts at the desired current - 2.8 amps for 12AU7, more for some other tubes.