I suppose with the concept in mind that if you believe a volcano is 500+ z levels deep, landmass dropping with obsidianization would take a long time to see returns to the useable surface level in placing and operating the power networks and pump arrays to make it relatively non-dwarf laborious or prone to error. With time you'll have a tube that is hopefully as well formed as you'd hoped, but possibly longer than the lifespan of the fortress to arrange compared to quite normal underground digging, or dropping say 300 layers of choice-select unobstructed natural stone into the magma sea.
Also for actually cutting through volcanos with bridges maybe to make a 'capstone' from a lower position to hold a portion of your tube, you'd have to first drain the lava so its safe to construct the bridge with a controlled run-off while ensuring the lava spreading out and getting higher from below doesn't interrupt the builder, which over the wide z area, is a bit of a head-scratcher and highly dependent on how competent a DF fluid engineer you are, and your local site geography.
- Problem being for your diagrams is that bridges start off already extended, then can have their directions set to none (retract and dissapear from view), or directionals which pull them up into walls, which means they must have the room for them to extend-over, rather than springloading a upright gate which is then suprise-dropped as soon as there is enough room to accomodate it.
Alternative examples of obsidianization projects are like laying concrete in a multi-story building, (casting on site or moving it into a more adequate place in a controlled way), with the consideration that every piece of the bridges holding that lava in place must also be magma proof, or the heat will melt the most vunerable part first (the blocks or the mechanisms) and deconstruct the bridge.
DF has loose physics in that not all of those supports in the diagrams might not be needed, which could easily be moved to a ring of scaffolding to dock the pumps as long as one solid piece connects to a surface. Even in this diagram you could create a psuedo natural feature out of obsidian by control collapse by retracting the bridge with the obsidianized stone (cutting it loose to bear only on the bridge) or de-activating the supports (means rebuilding everything you toppled), which is the mechanics of a landmass clump-up that those 9 theoretical levels (water and lava held seperate, mixed evenly, then prepared) becomes 3 natural stone condensed ones at the bottom, which is a drop in the ocean before plugging 500+