We drove to Toronto few months back, via Buffalo, with just the 2 documents you mentioned above (GC & Nepali passport) plus obviously a valid US Driver's license. At Canadian side besides looking at the GC and Passport, she asked us where you going, how many days, any alcoholic beverages on the car? Since we had just visited Nepal recently, our Nepali passports had the recent I-551 endorsements, I guess. But I think it will still work if the endorsement is old (like from the first time entry).