So I guess the lesson here is, don't leave masking tape on your windshield for ten years? What a mess:
Fortunately naptha does an okay job of removing prehistoric tape adhesive, and is safe to use on plexiglass. But it's a slow process and it takes a ton of elbow grease.
It took over an hour of careful rubbing with naphtha-soaked shop towels to get to this stage, and there are still tons of little goo-particles stuck around the base:
Now it's finally clean, and I can quit sweating into a respirator mask:
I re-protected the windshield with an application of 20 mil PVC pipe wrap tape, which is known amongst the RV community to be safe to use on plexiglass. It's also quite thick, so to avoid fitment issues I used regular blue masking tape around the base where the fairing will go.
As long as I remember to take all this off again within the next few months, I should be able to spare myself another round of goo-cleanup.