The Code requirement, for good reason, is all conductors must be in the same cable or conduit. I'm not sure whether conduiting this route and stuffing old cable and new wire in the conduit would suffice, that would be up to the local inspector. The conduit would have to be quite large because it would be a nightmare to pull, and because the flat 6-2 cable gets treated same as a round wire of its largest dimension. With 2 "wires" in the conduit, "wires" can only take up 31% of conduit cross section. One thing conduit would be very good for is allowing easy adds and change-ups, extra helpful if you're mudding up the walls! Metal conduit is allowed to serve as the ground wire.
However I would re-cable with 6-3 rather than risk having the inspector redflag it and have to bust out drywall to fix it.
There's no reason to tear the 6-2 out of the wall, unless you have another place to use it (not outdoors, mind). Just bring it into a 120mm (4-11/16") junction box ($2.50 at electrical supply, $5 at big-box) and cap it off at both ends. It can be used later for welders, or EV chargers whose labeling/instructions allow use of a 6-20, 6-30 or 6-50 connection.
You have this. You needed this. Note how many lattés there are in the price difference. I like to use frappucino's (or pizzas) as units of cost savings in cases like this. This case is a glitch, on my screen it shows a $0.02 difference and I suspect normal pricing would put it at 30%.
I find inexperience + savings seeking = this kind of error. A lot. Before you seal up the walls (why do that at all?? It's a garage) I suggest searching for where else this might have been done.
In both the examples you linked, you have lifted out of context.
- The "retrofitting a wire" case, two things wrong there: first it applies only to ground wires, which are a different case because they are not conductors; grounds only carry current during emergencies. And second it applies to old work that was grandfathered because it was legal at the time it was installed. Some people think grandfathering is amnesty for code violations. It's not.
- In the neutralless 14-50, that case talked about the plug, not the socket. That makes all the difference in the world. The plug is free to take only the conductors it needs, but the socket must proffer all the conductors that its design implies. A neutralless 14-x socket could actually cause a deadly problem if you plug in an appliance that had formerly been wired for NEMA 10.