You're right about this and your vase being wheel cut, probably with copper wheels. Copper wheel engraving employed wheels in a wide range of sizes, from pin-head to several centimeters, and were used with a slurry of oil mixed with grit (pumice in the old days, now carborundum) of various grades that did the actually grinding. There were also stone wheels employed and later diamond-embedded wheels; these generally remove material faster but don't achieve the same sharp details that copper wheels can.
Sorry I can't help with dates or makers.