One other option..but not as good as a video camera with XLR inputs...
I also have a Canon 5DIII that I occasionally mount a small condenser mike on when I want better sound than the built in mike. The Canon 5DIII is a great camera but can't do sound wise what my Canon XH A1 can do with the quality of music sound.
You can buy less expensive DSLR cameras(i.e. Canon Rebel) that record HD video. However, without an external mike...the sound is not the best.
And when I say sound...voice is no problem for most cameras..it's the quality of the sound of the music that suffers with less expensive cameras.
If I was doing videos that I wanted a good music sound on I would look for a used video camera that had XLR inputs so I could mount a good mike to it.
Here's a link on Ebay...not sure of the quality of the used cameras but it's worth a look.
http://www.ebay.com/sch/i.html?_from=R40...mp;_sacat=11724Sometimes you can find a good used one in a camera store.
Again, best of luck.