I'm thinking about how to do this with minimal disturbance of the K&T. In some ways a response to @Ecnerwal's answer, but won't fit in a comment.
If you cut back the wall hoping to install junction boxes and then extend the cables back to a panel in the existing location, the problem you'll face is this: The way K&T is usually routed each one goes off by itself through a nearby tube with no slack. You cannot bunch/group/reroute the K&T wires the way you might do with NM or BX. So you'll have to put in a junction box for each one of the 16 branch circuits. But those boxes have to be accessible after you're done. You could end up turning the entire wall into an array of junction boxes. You won't know how easy or hard or ridiculous this will be until you open up at least about 20 sq ft of wall.
I'm trying to imagine a slightly different approach but a bit stuck on details. Build a junction box in this location without disturbing any of the branch wires. Remove the feed wires and the fuse blocks. Somehow line the existing box around the existing entry tubes, without disturbing them or their wires. The thing I can't see is how to do that in a code-compliant way. You can't build your own junction boxes. But it seems like the only practical way. In this box you'd splice everything, carefully to new cables that go to a new subpanel nearby with its own new feed.
I think you could probably (hopefully) feed that whole subpanel with a two-pole 20A AFCI breaker and then use 10A breakers for all these circuits. If any of these circuits needs more than 10A you should adjust your loads to stop doing that. Don't stress your old wiring.
And a final thought: If the house will be sold in the next several years, I think it should be part of the buyer's budget and plan to do a once-per-century rewiring. In that case I don't see the point of hacking this.