As I said before, this reduces to a word game. Using the label,
relativistic mass, has been dealt with repeatedly as an outdated description of momentum. Here you seem to be just substituting
active gravitational mass where relativistic mass would have been used. You cannot correct faulty reasoning by just relabeling things.
It has been argued (and is generally accepted) that the momentum of a massive object, which is a fundamental component of its relativistic mass, does not change its gravitational mass. Where the idea that any momentum of a massive object does not change its gravitational mass has been discarded, it is flawed to assume that the momentum of a massless photon, does result in gravitational mass.
It is far more likely that the momentum of EM radiation, here referred to as a photon, is the result of the interaction between the EM waveform and matter, where both momentum and the quantifiable particle character we refer to as a photon emerge from that interaction. Yes, what I am suggesting is that the particle character of the photon is emergent rather than inherent.
The first page of the link you included, results in a google search, that is filled with links to discussion groups and blogs, with one exception, a paper
The rest mass of a system of two photons in different inertial reference frames: 0+0=0 and 0+0>0. A paper published at arXiv in 2007 which appears to have been cited by no other papers since. I have not read the whole of that paper yet by it begins with,
"We show that the rest mass of a system consisting of two photons is a relativistic invariant having the same magnitude in all inertial reference frames in relative motion". Granted an abstract is not a complete description of the authors' intent, but is does begin both with what appears to be an association between relativistic mass and a system of two photons.., not individual photons...
Farsight's, your statement above,
A photon has a non-zero active gravitational mass and a non-zero inertial mass, but a zero rest mass. can be read as decoupling the relationship between inertial mass and the equivalence principle, where it is a massive object's inertial resistence to accelleration that is compared to gravitation.
You are just using the term
active gravitational mass in place of
relativistic mass, in an apparent attempt to hold on to the historical concept of a fundamental association between mass and gravity and the extend that fundamental association to energy.., or the photon.
The mechanism of gravity at a fundamental or in terms of quantum quantum gravity has not yet been worked out. But I at least am fairly certain that attempting to hold on to archaic concepts like relativistic mass, by relabeling it as active gravitational mass is not the answer.
Do photons contribute to a gravitational field? At present the way we theoretically interpret what we observe of the universe at cosmological scales, suggests the answer is yes. But that does not automatically lead to the necessity of any photon mass, active or otherwise. What it does lead to is a need to better understand the emergence of gravitation as a quantum phenomena, with classical implications.