I was told that I should just run new 6" stove pipe to an 8" increaser at the thimble. I'd rather buy a better stove and not spend any money on the chimney/liner if it's not necessary.
Venting a "better" stove in an oversized chimney just makes it a much worse stove. You will need a liner to have any modern stove function properly. The 30NC is a really good stove with great customer support, just not the nicest to look at (unless you like big honking steel stoves). However, it needs a hearth with a 1.5 r-value; not sure what is under the stone in yours. Btw. You will also need at least 16" of hearth clearance in the front, even for that old BK.