Can I add a separate neutral wire to my cooktop/range circuit?
That &quot;sistering&quot; is called paralleling and you can't do that, as a lot of bad things can occur, including a fire.
Further, you cannot run just a separate neutral wire even if it was the right size. That's in NEC 300.3 -- all related wires must be in the same cable.  There's a very good reason for that -- electric wires kick massive EMFs, and as long as the wires are together, those EMFs will cancel each other out.  If current is going in a loop (out one cable back the other), then anything between those cables (e.g. cable staple) becomes the core of a transformer, and heats up. It also causes vibration (the F is for Force) and vibration causes metal fatigue, cracking, overheat and arcing, which starts fires.

I'm sorry you did not install the proper cable, but you also did not read the instructions.   NEC 110.3(B) says you must install the equipment according to the labeling and instructions, which obviously implies that you gotta read 'em LOL.
Unfortunately my best suggestion is to chalk the wire cost up to &quot;tuition expense&quot;, buy the right thing, and proceed from there.
If you can't sell the 6/2 on Craigslist, I would advise leaving it in the wall in case &quot;the next guy&quot; decides to go back to separate oven/cooktop again.  Ovens need 6/3 for the oven light, but cooktops generally only need 240V so 6/2 is plenty.