WTB: 4.77 ring and pinion
 

anyone have one or similar?

You need the front diff out of a 4x4 Kia Sportage, which isn't going to be fun to find. Or order the gears new from Kia, which is what I did - I found them for <$300 BNIB.

when I search for them on car-part.com it asks for either a dohc or sohc engine. Does anyone know if there is an actual difference in the front diff with either engine?

You might try perusing S2000 forums or even posting a WTB there. 4.77s seem to be way more popular with S2000 guys than miata guys, or at least they were when I had my S2000 years ago.

Local u pull it has two of them for $35 each. But I would rather pay then lug my tools, and roll around in the dirt in a sketchily lifted car for a couple hours. New one on eBay for $175 shipped. Used for $150 shipped.
Not sure I want to deal with breaking in a new one because it's a race car. I can't just go drive it around

Wow 35$, I would be wrenching ATM if I was you. If you go and want to sell the second one, let me know.

I ended up just ordering a whole carrier with only 20k miles for $150 shipped

Where did you order ?

Ebay.
Search for Kia sportage front carrier.