Looked at it in the light of day and did some measurements. I needed less than an additional centimeter of clearance.
The Vetter fairing seems to have a ABS shell, and the black plastic trim on the front of it is a separate piece.
First I removed the headlight and the headlight bucket. To remove the bucket, you have to adjust the headlight up/down adjustment until it is no longer attached to the bucket. Then there's a bolt on either side. After that, it's just pulling it out.
A few holes already in the trim, so presumably that isn't meant to be waterproof. A quick caliper measurement shows about a centimeter of space behind it. Encouraged, I removed the trim.
I took a hole saw to the trim, made two holes, and filed it down with the rasp. Plenty of room for up/down adjustment now.
I then reinstalled the trim. Note this requires removing one of the rubber mounts to get the trim back in. PITA to do.
Everything works.
Here's some before and after shots. Note I think my camera apparently auto-adjusts brightness. In reality, the LED is a lot brighter - took it on a short test drive and it does make a large difference.
Old halogen bulb is on top (Wagner Britelite 9003 bulb), new LED bulb is on the bottom. Low beam to the left, high beam to the right.
All in all, for $30, I'm pretty happy.
Am a little concerned about the socket though - even with the stock setup, it looks like it is in a good place to get shorted out by rain. I may want to address that sooner or later.