"Photon flux density actually is a measure of the rate of flow of light in a given period of time. It is measured in Lumens."

No, it is not measured in lumens, at all. Lumens is weighted at 555nm. Photon flux density is measured as umol/m^2/s-1.

"Also, published Flux Density rates of various light sources do not take into account the direction of the flow of photons"

Photon flux is a ray, and as such, straight line emissions from the source, and reflection from a reflector happens at the same angle at which it strikes the surface.

"With this in mind, a well designed T5 running very cool and being able to be very close to its target can actually be more efficient than a "hot" light that has to be many magnitude further away"

Can be in theory, in almost all practice, it fails. Also, do you understand orders of magnitude? Your use of the word hints that you do not.

"I may be new to growing, but I know my science."

Speaking as a research director, your science is totally flawed and incorrect.

Time to put my own hip waders on, it seems.