Most "dense" caulking / filler to fill small gap in ultra dense wall?

[666666]

Just finished building a "room within room" structure, everything is ultra tight, ultra dense. All framing and sheetrock is overlapping at all points, sealed tightly, etc, a lot of attention was paid to making sure that every square inch of the walling systems have equal density, no "gaps", "leaks" or "thin spots", etc.

Except...... I just found one small gap... had a professional carpenter hang a custom door, he was instructed to add jambs directly to the frame so that no gaps existed, however, in the name of getting everything straight and functioning perfectly (because a few dimensions had changed slightly along the way for certain reasons), he apparently felt a need to shim out one jamb by about an eighth of an inch. So, on my "outer" room, the entire walling is of perfect uniform density EXCEPT for this one 1/8" gap at the jamb area. The job came out so nice that there's just no way I'm gonna rip it apart and redo it. My only option here is to FILL the gap.

So my question is, what is the most "dense" caulk or putty or filler I can possibly get at say Home Depot or the like that will allow me to fill this gap and achieve as close to uniform density as possible? Sheetrock spackle? Sidewalk crack filler? some type of wood putty perhaps? (Note: the outer walling density: one layer of 5/8" sheetrock and one layer of 1/2" sheetrock, Green Glue in the center.)

Normally I use good GE silicon to caulk / seal things around the house... but this stuff does not appear to be very dense. Makes a good air-tight seal though... very flexible and durable.

Sheetrock spackle seems like it may be fairly dense, but the downside is that it could crack and crumble out of a "large" gap over time... or maybe not.

Or unless I pressed in some sheetrock spackle first and let it dry, then went over it with some silicon to ensure a good air-tight seal...?

I know that "acoustical caulk" is often mentioned around here, remains "wet" etc, but I don't know if this is what I want for this specific case. A solid hardening filler should be just fine for this instance I'd think. No need to "decouple" the jamb from the frame, it's screwed tightly onto the shims anyway... just looking to merely fill a 1/8" gap with some type of dense material.

Thanks!

[seven]

How about Electrical Conduit Putty?