If you're gonna use cord instead of strapping (some of us have to use cord like in the case of a 60's P83) you may want to consider changing your wires to a brand that has built in eyelets in the string holes. This will eliminate any sharp edges. Also, just a speculation, but along with rough holes your problem could be with those 40 strand wires . I would think that would put a lot more tension on the string than a 16 or 20 strand.

Buy a good quality cord. Sailor yacht cords are made of very durable fabrics.

In case such thing happen and there is no way/time to replace or play with different snare - stick the wires to the head with duct tape. At least snare will "sound like a snare" somehow.

I just replaced all of my P83 and 85 strainers with P86's. So far I love them. The hole spacing is the same but I did have to drill the holes out a touch for the new bolts. I will say that while the engraved strainers look pretty good on my '65 Jazz Festival, a series 400 Supra, a '64 8x15 concert snare and my 6.5 BB, it is a little austentatious on my Acrolite Standard. What I noticed when taking off the cord from those drums is that all the Gibralter cord was very frayed (and it was all new) but the 2 pieces of old Ludwig cord (the red cord) was still in very good condition. From that I would say that I would suggest Ludwig cord if you are using cord.

As a side note, I just purchased 30' of 5/8" black grosgrain ribbon at a fabric shop for about $6 to use in attaching snares. Fabric straps for a single snare drum run between $3-$4 at a music store. The ribbon is the same fabric I believe. 30' will last for as long as I can keep from loosing it and it works WAY better than cord or the nylon straps.