[gmarx]

You don't need an outside offer to ask for a raise. The cap for raises is nonsense. It may present a psychological barrier to your manager but mostly it is a prop to point to; so your manager can say "not my fault- see there's a sign that says no raises above 10%". The trick is they can give you more than 10% if it involves a promotion. The other trick is that raises are difficult to ask for.

You have a cogent argument for a promotion and raise. Ask for it. Present your argument minus anything that could be viewed as a threat (like interviewing at Google).