A belated welcome to you! First place to check is with Brad the old tool nut 1959 ( IIRC) on eBay. He has TONS of vintage tool items ( and other Americana stuff) on his shop- He has a beer can in his photos for scale; a Pabst Blue Ribbon I believe.
Send him a message via the contact seller option. Also religiously hunt the internet by searching Reed 3C vise parts as one will turn up in due time.
You can also post a WTB on the GJ classifieds and search said classifieds for the criteria “Reed 3C.” It also is prudent to sift through the vintage vise thread here, looking for leads or members with alot of Reed projects on their hands.
Good luck, and be persistent.