The color-mixing nodes have lots of options for how to combine the two (R,G,B,A) data-streams that are presented to them. Look them over and you’re sure to find one that does the trick.
I suggest mapping-out a “compositing data plan” (my term …) with a pencil-and-paper to watch carefully where the numbers actually need to go. Pay particular attention to the light, especially the specular or highlights. If you have two streams of data, both of which need to be visible in the output and both of which include light above-and-beyond what is needed to illuminate them, then that light is going to show up twice and it will therefore be very bright indeed.
“Blur and glare” can be problematic if applied, so to speak, “upstream” in the data pipeline. You can easily wind up with a result that’s unnatural-looking when combined with something else, because the pixelation that produces “blurry” or “glare-y” also must be combined somehow. This can produce all kinds of problems … “rings” around things, too-bright areas and so on. You might need to instead do that “downstream.” For instance, first obtaining a result consisting of “the blackboard minus the chairs that are in front of it” (so that you get a clean separation), then applying effects to that result, before finally blending the various pieces together.
I’ll usually try to plan out how I’m going to “comp” each shot, then throw-together an example using cubes to prove the concept, and of course, file-away that blend-file somewhere where I can find it again later. You really need to know that what you spend hours producing will work when the time comes, and you need to know this first.