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I am not sure if you could use a thru bolt to re-attach the mast base. It would depend on if the bolt could freely pass completely through without needing modification. I'm pretty sure that's a structural part, so I'd advise against modification. I looked at my base and it looks like you would have to modify the hinge portion to use a single bolt. You MAY be able to use 2 bolts though, putting the bolt head on the inside and the nut on the outside. I'd check to make sure it all fits well and that the hinge freely fits into the base before fully assembling.
I would go with your assumption about replacing the broken part. Both the mast base and the hinge support the mast. If either fails, the mast will likely come down. I'm a firm believer that any damage or breakage should be fixed or replaced in any case. You don't want to be stranded out on the water or to have a failure that will cause more damage that will need additional repairs. Or worse, having that failure cause injury.
West Coast Sailing sells both parts but are temporarily out of stock:
Mast Base:
https://westcoastsailing.net/hobie-18-mastbase-casting/Hinge:
https://westcoastsailing.net/hobie-18-mastbase-hinge/After a quick google search, that was the only place I could find that sells the base. The hinge however is sold at many places, but all I checked were out of stock. Maybe a used one on EBay if you want it ASAP? I didn't check...