We ran into the same problem with a Napa sourced assembly which wasn't even close. I was able to obtain the correct "flat diaphragm" pressure plate from a local source for a 57 V-8 truck and a core wasn't required. Clutches Unlimited in Midway City, CA 714-373-6155, likely has one for your application as well. I'm sure there would be shipping costs. There has to be a clutch rebuilder in the bay area. That would be my first recommended option.
Fred


1956 3100 Pickup/Red/350/3sp OD/PS/Disc Brakes
1957 Bel Air Sport Coupe/Red/355/TH350/PS/Disc Brakes
2017 Silverado LT Single Cab SB/Black/5.3/6 Speed Trans
1947 Willys CJ2A w/F-Head engine