So I finally did have success getting the airbox cover out of the bike frame from beneath the gas tank without having to remove the gas tank, but it was not easy, so I thought I'd share my experience and some images from it, since everyone has been super helpful to me, and now I finally have a bit of experience that I can contribute to the collective tribal knowledge of Guzzi wrenching we have going here. Hopefully this can be some help to the next guy or gal who finds themself struggling with this task with this pretty niche bike.
Again, it's a 2010 Moto Guzzi V7 Classic.
First off, definitely start with this super helpful set of instructions from Joe:
https://flickr.com/photos/sign216/11470971416/in/album-72157638864403325/Here's what I'd like to add to those:
I had to separate the airbox cover into its two parts. I couldn't fit it out of the frame while it was still put together. Joe's instructions say that separating these two pieces isn't necessary, but I couldn't figure out how to get the cover out without taking it apart. And even if it is possible, separating the pieces just makes it a little bit easier. Of course, you have to get the two pieces unscrewed from each other while they're still inside the frame, and you may need a flexible shaft screwdriver for this (as indicated by Joe in his instructions).
After separating them, the "Cover" (part #:GU32113410) will come out easily, but watch for the gasket which may fall out. The "Filter cover" (part #:GU32116910) is going to be the thing that gives you trouble.
I will say, disconnecting the regulator entirely made it easier to set those cables aside, and gave me some much needed additional room to maneuver the filter cover.
Grand finale: see pics below for the orientation needed to slip the filter cover in and out of the bike's frame without forcing it on any side. You want to extract it from the left side of the bike. You want the front of the filter cover facing down, and the top of the filter cover facing the right side of the bike.
I appreciate everyone's input to my posts and questions, and offer this tiny bit of wisdom from experience in the spirit of gratitude and reciprocity. I hope this helps the three other people in the world riding around on V7Cs.
And just for fun, there's a pic of the bike on the ride I took it on later that day, complete with blue pipe heat damage from that time I rode it on one cylinder.
