@Colgate2004: not sure why you stumbled on the NEMA 6-50 installation guide. For as long as I can remember, and I just checked the website again, Tesla recommends installing a 14-50 receptacle, and it clearly states that the gen 2 UMC cable comes with 14-50 adapter.
If you're like me and intend to keep your UMC semi-permanently plugged into the receptacle, you should just return the 6-50 and get a 14-50. It's $7 at Home Depot. Or you can get the 6-50 adapter for the UMC from Tesla for $35.
Big caveat is what kind of wiring you used. If you used 6-3 Romex (or a THHN solution with 2 hots, neutral and ground), you're good to go with the receptacle replacement. Otherwise, you're likely missing a neutral wire that the 14-50 requires.
And like others said, get the 50A breaker. The one I needed for my panel was $8.
I envy your panel-to-receptacle distance. I had to do a long run of 6-3 that required some fishing thru walls.
One last thing to note: I charge my car at 20A because there's a noticeable drop in voltage when set to max (both with gen 1 and gen 2 UMCs). Loss in voltage is due to resistance in the circuit, which manifests as wasted energy (heat). I tell the car to pull slower, and there's less resistance, which means more efficient wall-to-car charging. Part of this is due to my long run of cable, but you should check if you are getting voltage drop, and reduce your amperage on the car end until you see things return to 240+.