I think you could lose your shirt on this job with that fixed price. Often with K&T, if you so much as bend or otherwise disturb the wire the insulation disintegrates and you are now back to square one. The existing device boxes may be too small for the addition volume of another conductor.
Fishing new NM cables in a building with balloon construction shouldn’t be too bad. You can often fish new feeds alongside the chimney right up to the attic.
Just a thought, but I think if a permit is going to be pulled for the job, as it should be [CYA], the inspector might as well be consulted ahead of time as to what he thinks, as that is likely what will make or break the job. That also puts this job on his radar, so that it will be more difficult for the HO or GC to award the job to someone that has undercut legitimate bids because they are unlicensed or otherwise working without a permit.
