Really, if the existence of a dragon is the issue, there's always the lacrima route. That's how Laxus and Cobra got their magic.

As for the different magic part, I don't see everyone issue with it. Just because the element is similar or the same doesn't mean the magics are. I would think two makers of a different element, wood and ice for example, would be more similar. But then again that's just me so it really comes down to GMs