A 20amp receptacle can accept a 20amp plug, which could overload the breaker, which is why the National Electrical code says you can't do it. I would stay with the 15 amp receptacle. If the new receptacle keeps tripping then there is probably a small leak of power between the conductors. Some GFIs do get weak and some are probably too sensitive from the start. I wouldn't put a 20amp in, even though I have never used any appliance with a 20a plug, and not many people have, it would still be best to stay with the correct receptacle. Since the receptacle is designed to trip with an imbalance of current on the conductors, increasing the load capacity of the receptacle shouldn't change whether or not you get nuisance tripping.