Okay.
So we build a basic fiberglass packed frame. Then add a cross brace in the center, using wide enough boards that let you overlap them, use a few runs with a dado on each to pocket them together, then pack with glue. Doesn't need to be studs. Heck, doesn't even need to be dimensional boards. Some spare 1/4" plywood should be enough for this. After it dries, we drill a hole through it dead in the center. This will be our mount.
Next we try to find the right way to mount it. If we drill the hole the same diameter as a mic stand's threaded end where the mic clip clips on, then we just use the locking nut to secure the cross brace to the mic stand. You could even countersink the underside of the cross brace if needed.
If your brace and insulation assembly isn't too heavy, then you could try one of those flexible goose necks. Or use a drumset accessory clamp like this:
...and then buy a used mic stand to steal the boom arm:
...then use the clamp to hold the boom arm to the side of your existing mic stand.
Now, as I think about this, you would have to have the deflection filter mounted perpendicular to the ground, to have flat against the singer's face. So a boom arm at an angle might not be perfect.
So, instead of the mic boom arm, let's use a cymbal stand's boom arm. Drill a smaller hole in that cross brace just big enough for the cymbal stand boom's cymbal stem to fit through, then tighten down with the wing nut. Then clamp the cymbal stand to the drum clamp, then clamp to the main mic stand.
Should be simple to find a drummer with an extra beat up old cymbal stand they could donate to a worthy cause, or simply hit a pawn shop or two. Maybe the used gear section at a drum shop.