
Preventing "mulchy-mouth"...
I agree with J~Bird. As he said, water should definitely be "in the mix" (part of your gear), in this case to help resolve (lubricate) matters, once a foreign object is lodged. Yes, it's difficult to wrestle with a highly-likely panic response, but you must win that battle first. Within that brief, ensuing calm, lubricate to enhance success with the effulsion phase (pukin'). So, I'm saying I also agree with Huna in that regard.
Scary, yup... Did I mention that I googled "tree climbing" the night
after I attempted to deadwood a Red Oak at my home? It went like this: Warmed up a properly maintenanced 18" chainsaw; tied a ladder to the tree; tied a rope to the chainsaw; climbed the ladder to the limb; tied myself to the tree; hauled up the chainsaw; made the knotch cut, no problem; repositioned the saw for the back (felling) cut; pulled the throttle trigger and
completely filled my open mouth, throat, eyes, and nose with rapid-fire Red Oak confetti. As mentioned, in your story, CaliJohn, breathing was just not an option, and I couldn't see, and the chainsaw was running, and the limb (30') was falling.

Happily: I found the kill button; stopped and lowered the saw; the limb fell into the anticipated lay; I grabbed the ladder rails and "painted" the side of the tree with emphatic, baritone spittoonery, just short of pukin'. Only then, did I breathe. I worried during that moment that I would never belong in a tree again, and that I shouldn't be found in one unless I was thrown bodily into it. Thus, my climbing name...
I'm so thankful that I found "treeclimbing.com" and "treeclimbercoalition.org" in my first online search that evening. On those sites I rebuilt my perception of my relationship to trees. It has become something much, much greater than the mere success of deadwooding for my woodstove.
Another thought...
Prevention is of course a better solution. Please consider developing the following "dry mouth" prevention technique, promoted by some knowledgeable martial artists. It has worked for me.
o Keep your nose clean to reduce mouth breathing, but given that you must open your mouth...
o Keep the margin of your tongue gently positioned along the inside margin between your upper teeth and gums
o "Blow through your tongue"
o Doing so, your tongue will relent and re-seat, somewhat like a gill, acting as a physical barrier to macro particles
o Maintain contact with the tip of your tongue behind, not under, your upper, front teeth.
o Regain your normal breathing rhythm
o Return to nose breathing
DISCLAIMER: Consult your personal physical trainer about your own specific potential use of the technique described. No warranty, guarantee, nor affidavit provided, nor implied. Do not attempt this technique while "french kissing"
Climb safe.