I don't care what size of recurve you have, a griz is just too much for that type of bow.
Not exactly correct. There were a lot of griz, kodiaks and polar bears in the Pope and Young book prior to the invention of the compound. Recurves and longbows have taken game up to the size of elephants and rhinocerous! If you can handle the draw weight needed and select arrows heavy enough for the size and toughness of the critter - and have the stones to poke one of them bad boys with an arrow[:-] - a stickbow will do the job.