I'm going to go out on a limb here as this is I think my 2nd post. I've been a member for a short while. Don't be influenced by my user name. As a general contractor in CA I've overseen miles of electrical wiring and work. I have performed enough myself to qualify as a C-10 but I don't need that as I don't look actively for electrical work only. That which is incidental to the overall scope of the job is allowed under my license.
I was faced with a K&T rewire similar to the OP's situation. One thing about K&T is there is no such thing as a 'hybrid' wiring system that uses some K&T 'here and there'. The neutrals are likely to be spliced together kinda sorta following the individual hot wires, but sometimes not all that closely in the attic. You disconnect 100% of the K&T and cut it back, or wire the hots and neutral together, so it can't be used.
However, there has been some talk about using low voltage to power lighting fixtures that are all but impossible to rewire. Low voltage lamping has expanded nowadays to include some great choices including the simple retrofit of a 12v incandescent in place of a line voltage bulb. The NEC apparently does not address voltages less than 50v with a few exceptions. Placing a transformer in a way to pick up some of the wiring is something to consider. I suppose I would discuss this with the AHJ before commencing. Note: I have read Ch 3 extensively and this proposition is not clearly addressed. I looked into battery powered homes and that hasn't come into play much either.
Since this thread is mainly concerned with insurance, insulation and old codes, discussing this with an intended insurer would be very wise. There is very little info on the subject so this has to be a case by case alternative. Worth looking at AFAIC. There in only one consideration and that is the worthiness of the existing rubber coated single wire not combined with the other wire in a cable. Again, does that requirement apply?
In the end, we did not go with any low voltage but it sticks in my craw. If you have specific code citations that apply here, I think we could benefit.
One more thing: luminaires are required to meet UL standards in any scheme within architecture. That isn't hard to overcome if existing fixtures are taken to the appropriate facility to be rewired with an appropriate gauge. You might be able to do this yourself using UL approved wiring. I rewire corded lighting all the time using rated wire that is sometimes manufactured to look the part of old silk covered cord. I have never rewired an old fixture and installed in a job to be inspected. I'd like to hear about that as well.
Gentlemen (and ladies), thank you for reading.