Get that picture boldpaste2 posted, make a show picture command and that's just it.
The show picture method doesn't blend well as my only options are a difference blend, an additive blend, or an opacity (normal/alpha) blend. The blending portion of this is the important bit and it can't be done sloppily -- if it is, then the screen becomes unreadable.
Throwing a phosphor grid into the show picture command doesn't work well with any of the default blending modes: see the below images.
Spoiler
Normal (100% opacity)
Additive (100% Opacity)
Subtractive (100% Opacity)
What I'm looking for:

The only way this can be achieved is by literally recreating the RGS***,dll, or at best rewriting a bunch of it
You're mistaken. If I wanted to have a sound's volume vary depending on the distance I was from the emitting object I wouldn't have to go in to the core engine and rewrite the Audio module or 'literally recreate it'. The tools that I would need are already in the engine. The tools a coder would need to accomplish this effect are also already in the engine. I'm not explicitly asking for shaders and FBOs - I'm asking for an approximation of a visual effect accomplished by overlaying an image with particular, custom, blend settings. It'd probably run the fastest and be more flexible if done in a shader, sure, but I recognize that binding OGL/DirectShow functions and/or capturing the frame and messing with it and reinjecting it is something that's not trivial enough that somebody'd just do it for the heck of it as a request fulfilment.
It's not necessary to bind OGL functions into the game executable, hack up a new DLL to call OGL functions to/from, or even modify the core rendering system to accomplish advanced graphical effects in RGSS3. There are plenty of scripts which don't require or use custom DLLs/EXEs but still replicate effects that would normally be done through a shader because what we've got in-engine is plenty powerful enough to achieve them (if a bit slow).
http://forums.rpgmakerweb.com/index.php?/topic/13941-map-effects/
Even most realtime lighting scripts don't require particular DLLs -- though they would likely gain an immense speed boost from doing so as that would move the processing from software rendering to hardware rendering -- but this topic is not about that. There are many ways this could be achieved that I could think of that work decently, can't be done through events alone (or at least could but would require very particular and specific images), and also wouldn't require rewriting parts of the engine and/or binding/intercepting OGL/DirectShow stuff.
It is simply an effect they achieved through some videographics / cinematics effect.
Which is also what I'm looking for here. I don't need a physically-accurate CRT shader (e.g. Fallout 3, Alien: Isolation). I just need a decent visual approximation.