Strictly speaking the gravitational interaction of the mass of the system only propagates at the velocity of the photons themselves. The photons themselves are entirely massless - the conservation of the mass within the system contributes to their momentum. They definitely do not interact gravitationally and in the rest frame of the photon, you will find no field around them. If you do find a gravitational field around a photon, there's a Nobel prize in it for you.
Thus, they remain massless. It's a trick of mathematics that results in the interpretation you speak of - which while strictly speaking correct, is what in physics we refer to as a bit of a mathematical dodge, usually used to make computation of masses a little easier

And the PM you sent me - I've been recovering from a shoulder operation and am stoned out of my head on codeine. No offence taken.
EDIT: I should also note that momentum is not dependent on mass. The momentum dependence in special relativity can be attributed to both velocity and mass. You can start a huge row in most physics departments by claiming to be a proponent of one or the other.