The coulter disks are flat and are about 1/8 inch thick. The John Deere I used is a bit thicker than that but should work ok.
One thing, and this is where I'll need help from the experts here.
Your plow is a Dearborn and mine is a Ford. Some parts are the same and some aren't. I just don't know what parts will interchange.
The first number I gave you...
Scott or Alan may get you shins and shares, their parts are for Fords. The fact that the shins are totally gone may give you some trouble but the shares should have a number on them.
The link to crescent forge lists different part numbers for Ford and Ferguson and they say to call them if a part is not listed but I called their number and it is disconnected
I'm surprised that agri supply has left hand shins but even more surprised that they don't list right hand shins. Yes your plow is right hand.
You said you can't find any shares like yours, it seems to me that the shares on your plow are too small (short) and very worn. A new share, properly sized, and this is just my opinion, will be much larger and you may actually be seeing a share for your plow and just don't recognize it.
I know I'm not being much help here, I'm just talking but I've gone through this very thing while I was rebuilding my plow.
I sit at my desk most of the time and if you want, provide me more info on your plow and I can do some searching for you. Maybe I can come up with something.
Still, here on tractorbynet FWJ is the best bet for this sort of info.
This is a copy and paste from another website telling you about Scott. The first number I gave you
For Sale: Ferguson, Dearborn and Ford implement parts including corn picker parts and plow shares, moldboards and landsides, your old plow parts will have numbers on the back to identify the style you have. Price: Contact me
Phone: 717-896-3414 weekdays