Glyptodont - the OP was asking for a classical & baroque piece because his/her options are limited by a teacher or a music school (something to do with "ARCT"). Your suggested composers are all post-1900. In fact, they aren't really "out of the way" composers at all - Satie's music is commonly heard in recitals, and Mussorgsky wrote one of the most ubiqutous and commonly-played pieces in the graduate repertoire ("Pictures at an Exhibition"). The most recent recital I attended featured a MacDowell work (hardly obscure).
For REAL lesser-known composers, within the classical definition, look at Kuhlau, Clementi (sonatas), Weber, J.C. Bach, or Hummel. Hummel was once considered to be on par with Beethoven (though of course he's not quite there); he wrote some amazingly virtuosic (!) sonatas. Stephen Hough was on tour a couple of years ago with his F# minor sonata. Baroque-wise, if you're willing to look at the non-piano keyboard music than there are more composers than I can name. Not all were inspired, but there's a lot of great stuff there. How many of you have ever performed anything by Biber?