What a lot of Italians do is make a frittata with leftover pasta (lots of times this has egg as a binder), but they often just make something more like a spaghetti pie too. This wouldn't get rid of the crunchy on the outside problem, but the pasta inside would still be a nice texture.
I doubt 1-2 minutes microwaving would finish cooking half-done pasta, but then again I've never done it.
Do you cover the pasta when you microwave it? That would help. Use a microwave-safe plastic wrap on top, and don't seal it completely so air can escape.