Hello there!
Charlie already covered pretty much everything. But I have a 28-300 on a crop body myself and take moon pictures all the time. You can definitely get something sharper than this one, specially using a nice 2x TC I think, although I'm new to all this and never even used a TC myself haha
Now, I'm not sure what was the problem here, but maybe it was in the focusing. Did you use manual? If so, where did you focused? I usually go all the way to infinity and then use Live View to come back just a little bit, until I see the craters or details in good focus. Infinity doesn't work quite well for the moon, and neither does automatic... or, at least, not for me
Besides this, 1/15 is too low of a shutterspeed for the moon. Even if you don't see it, it's moving all the time and faster than you think. Get it -at least- up to 1/100th or more if possible. You should be able to get there if you lower your aperture. I agree f/2.8 should be enough, but it's probably better to take advantage of your lens' sweet spot. Try 'Googleing' it. If you're not going for the sweet spot, then keep it really wide to help get a faster shutterspeed.
From the EXIF data I see you've +100 Clarity, so I'm thinking this ought to look really soft w/o it. But nothing to feel bad about, it's not that easy to get the hand to photograph the moon. Takes several tries to do it good, and as someone said up there, try to avoid full moons like this. You'll get far better results when you have shadows there.
edit: oh and one more thing, try to take the pictures when the moon is really up in the sky and on really clear nights. If you could get out of the city, at least a few miles, that'll really help improve the clarity.