@daviecj
As a self-confessed keyboard oriented programmer, why are you focused on the file tabs anyway? Certainly, you do not use the file tabs to switch between files -- that requires using the mouse. The file tabs tool window was put in place as a simple solution for novice users or users who wanted a tabbed document view. It is not perfect, but it has served it's purpose quite well.
Look in the help (Contents > User Interface > Buffers and Editor Windows). Here you will find thorough documentation on switching between files and buffers, including the command names and default CUA key bindings for most operations. Most really keyboard focused users of SlickEdit do not use the file tabs at all. Instead, they use the buffer circle (next-buffer / prev-buffer) to swap between their most recently visited files, or they use Document > List Open Files (Ctrl+Shift+B) to bring up the file list and search incrementally to find specific files or to quickly see which files they have modified.
BTW, the only reason I could imagine that <Esc> new_file did not work for you would be if you are in VIM emulation, you need to use "Ctrl+A" to toggle to the SlickEdit command line -- <Esc> has specific purposes in VIM emulation. In all other emulations, <Esc> will toggle you between your current editor window and the SlickEdit command line.