I'm on a mac so I don't have "menu bar" problem since it's not part of the window. I guess it should not be a problem on Ubuntu Linux either.
I don't know if there's a sublime command to hide the menu bar on windows, if there's let me know and I'll add it.
I also don't know if there's sublime API command to run something on sublime startup. but we can remember the file you opened in Windowed DFM and if you open it again it can automatically goes to Windowd DFM mode. I've done similar thing in PlainNotes. Still not sure if it's worth the effort. it's too much work and in general will slow down your file opening in sublime.