If one's eyesight is good enough portrait will probably work fine. There are some zooming controls, I believe, but wouldn't work well because it doesn't go fast enough for page switching.
Amazon actually has some Kindle formatted sheet music -- mostly classical piano stuff. But, yeah, making it a PDF with the smallest possible margins, is probably going to be your best bet.
Note that page turns aren't super fast, so you have to get used to when you have to hit the button so that it will turn when you're ready for it. You'd want to rehearse with it for sure and not just jump on it for a performance.
I don't know of any 'auto' page turn, though, for text, you can set it to read to you and turn the sound down. I'm not sure that would work with sheet music though. And probably not with any PDF file.
Sleeping isn't usually a problem as the default time on the DX is 20 minutes vs. 10 on the smaller Kindle.
If you use it in landscape mode you'll only get half a page, but it will be bigger, but there will be more page turns. And sometimes there's overlap so one "page" actually is 3 pages in landscape.
Now, if you need to be able to see more than one page at a time, it's not going to work well. I play flute with our church group but sometimes I'm playing a written part and sometimes just improvising from the chords, or playing one of the choral parts. . . so a lot of times I need two, maybe 3 sheets easily available for my eyes to stray to. But we do have a guitarist in our group who, since Easter, puts all his music on his iPad. . .he sets it up for minimal page turns and it works just fine.