Played through the first three dungeons, did some exploring, grinded for rupees and got the bow and arrow (avoiding going the thief route as apparently not doing this gives you a better ending?), and am still enjoying the hell out of Link's Awakening despite the technical issues. Found more slowdown when picking up and throwing jars sometimes, particularly when at other jars to break them all at the same time. Still hasn't affected the game play.
Am assuming this is the same in the original, but it has been too long- if you don't want to steal expensive items, you can just grind pretty fast in the crane game. Just get the 50 rupee, leave, and repeat. Takes like 40 seconds each time.