Exactly. You just said yourself that you're getting wrecked by Falcon's grab game, which is true. Falcon has great combos out of his throws. However, since Falcon doesn't have many other approach options that are safe on shield, if he's running at you he'll most likely:
- Dash Grab
- Dance Trot
- Run up and Shield
You have to be aware of his options and know your options to punish them. Spot dodging, as you said, is an effective way to avoid grabs. D-tilt isn't great once he's actually in, I'll admit, but it can be used to hit him out of a run (as long as you mix up).
I'm not saying you won't get grabbed but you can do stuff to make yourself not free to grab.
Are you saving your jump before you up b? If so, you really shouldn't be getting gimped by Falcon. Falcon can kill you with his Aerials, yes, but you should be able to recover from pretty much anywhere otherwise...
Don't make your recovery predictable. Mega Man has really good Mixup for his recovery. You can try going diagonal below the ledge one time, directly below it another time, going low enough that rush won't get you back but your DJ will, you could go high, jump + air dodge back onto the stage to avoid any aerials, etcetcetc
In general, it sounds like your trouble here is that Falcon does a lot more damage than Mega Man. He does. A lot of characters do. Falcon however has the blessing (for us) of a weak recovery. Instead of focusing on getting CF to kill %, focus on getting him off stage and exploiting his weakness for everything it's worth. Mega Man has so many edge gaurding options that you can use that Falcon should rarely know what method you're going to use to gimp him.