The most likely cause of what you are seeing is a broken wire when the plane was originally assembled. The wire was pulled back a few cores and the end stripped. New wire was soldered to old, insulated and then they continued threading in that wire. Over the years the solder joint has degraded or the wire broke at the stress riser found at one end of the solder joint and now you have an open circuit. I've not heard of this kind of problem on the Straight 8 but that may be due to the rarity of the processors. It is apparently a fairly common failure on the 8I core planes.
As was stated you have nothing to lose in attempting a repair as the core is useless as is. A steady hand, good desoldering tools, lots of photos and you should be able to take it apart, effect the repair and re-assemble. Keep in mind that the core beads themselves are extremely fragile so take precautions that nothing gets dropped on it. Broken core beads are pretty much a death sentence to the memory. Replacements are unobtanium and if you decided to make the beads you would have trouble matching the originals well enough to tune the core to work with both new and old. You would end up making a whole new core assembly consisting of 49152 beads. You would need to be really determined to attempt that. I did come up with an idea that is simply too dangerous to try. Connect a power supply to the ends of the wire and ramp up the voltage until it just starts to conduct. This could be several hundred to several thousand volts. As soon as it starts to conduct the broken ends of the wire will start to heat and the moment the current starts to shoot up (the resistance drops) you need to cut power. You will have welded the broken ends of the wire together. The problem is that if anything goes wrong you are in worse shape than now and you really only get once shot at it. And the assumption is that the broken ends are in close proximity. Here is wishing you a steady hand and lots of luck! -- Doug Ingraham PDP-8 SN 1175