I would suggest asking the AHJ to see if they will allow this. I've been told that many AHJs are receptive to upgrade situations where a little money gets people into a safer condition (and closer to compliant) than they are in now, and where more money isn't available.
If it were a case of an existing wall outlet on an ungrounded 15 amp circuit, replacing the receptacle with a GFCI would be an improvement (as I understand it). IMHO, that's better than doing nothing at all. This situation is a little different because you'd have to tap the light circuit (which is already used for receptacle power purposes, anyway), put in a new box, etc. But in terms of the improved safety, it's the same.
I've seen a number of old houses around where the electrical is in terrible shape, but because it was compliant when installed, the AHJ has little power to force a change (that in many cases would do no more than put a family on the street, which aside from imminent danger situations would not be politically good). So it seems plausible to me than many AHJs would be glad to see an incremental improvement towards code compliant and improved safety where otherwise nothing could get done.