Except that your J-box with the NM cable is now inaccessible 310.15.
Did you mean inaccessible 314.29? Is the attic Accessible? If it is this would be OK.
And you still wouldn't have the ground required by 410.44, assuming the luminaire has exposed metal.
Wouldn't he be in compliance with 410.44 Exception 3. IF he adds a GFCI device at the fuse box before the load, or add a GFCI breaker. You will never find a receptacle to replace with GFCI due to box fill and receptacles are usually all end of the run since splices are in walls.
Of course you could splice as you are suggesting and extend the K+T with 90?C THHN per 394.10.
Do you mean just THHN not NM-B?
I think bringing it into a box in the attic is the best bet if it is accessible. 394.56 prohibits inline if thats what you meant. Splicing to THHN not in a raceway sounds iffy however 394.2 states single insulated conductor, thats THHN. If you had to do that I would use singe conductor UF like they used to use to feed ceiling heating cables or at least #14 XHHW-2 copper. Most supply houses will not stock these. I suppose you could solder a western union splice to get around 394.56.
I have been known to apply heat shrink tubing to the type R conductor back to the first knob, then re sleeve it with the tubing. Heat shrink tubing is UL listed as 105 deg insulation. If you do not have enough conductor to enter a box that is a problem.
Most saw shops can carbide tip a 3-5/8 hole saw, combined with 1/2 of a basket ball to catch the dust you can cut the lathe and plaster to install a 3/0 cut in box.
If you work on old houses often see this report:
www.nfpa.org/assets/files/PDF/Research/RESAReport.pdf
Page 47 deals with fixtures with 90 deg wire on type R wire.
They list type R as 60 DEG insulation.
I have a old 1930 Grahm Renolds catalog that lists type R wire.
I thought it was 85 deg C rated.
I see more problems with 1980's 60 deg NM than knob and tube.