You fish in dark waters. For one thing, the "mass" that photons lack is what we call "rest mass". Any material body, such as a proton, electron, atom, molecule, or slug, if you only can slow it down to zero velocity (from the point of view of the observer) will have a particular, measurable mass. Items such as photons cannot be slowed down, nor speeded up, but only changed in energy content, which is reflected in changes in frequency, and accordingly, in wavelength.

If you keep removing energy, you will find that it will not come to rest until all the energy has gone, and the photon will have gone too – it has zero rest mass.

Moving at light speed, it does have a certain "mass equivalent" which we can describe as momentum. The full mass equivalent of a body can be expressed as, not simply

E = mc^2, but as e^2 = p^2c^2 + m^2c^4.

Here p is the momentum, and in discussing a photon, m = 0, so we get e = pc.

So you see, things become tricky; one needs to have the precise mathematical definition and context.