Replace the vmparams file in the Starfarer install directory with the following:
java.exe -server -XX:CompilerThreadPriority=1 -XX:+CompilerThreadHintNoPreempt -Djava.library.path=native\\windows -Dorg.lwjgl.opengl.Window.undecorated=true -Xms512m -Xmx512m -classpath janino.jar;commons-compiler.jar;commons-compiler-jdk.jar;starfarer.api.jar;starfarer_obf.jar;jogg-0.0.7.jar;jorbis-0.0.15.jar;json.jar;lwjgl.jar;jinput.jar;log4j-1.2.9.jar;lwjgl_util.jar;fs.sound_obf.jar;fs.common_obf.jar;xstream-1.4.2.jar -Dcom.fs.starfarer.settings.paths.saves=..\\saves -Dcom.fs.starfarer.settings.paths.screenshots=..\\screenshots -Dcom.fs.starfarer.settings.paths.mods=..\\mods -Dcom.fs.starfarer.settings.paths.logs=. com.fs.starfarer.StarfarerLauncher
After that, just disable fullscreen in the launcher, set the screen resolution to your native resolution, and there you go, fullscreen borderless windows. :)
Alex: if you want to add this to Starfarer natively, the relevant launch parameter is -Dorg.lwjgl.opengl.Window.undecorated=true