Is there a way to enforce a line shift in the exported tab? It would make for a cleaner, more organized look, having the option to start each section on a new line.
Nice suggestion, one idea would be to map the Hookpad line breaks with breaks in the score. Looks like this is possible in Lilypond LilyPond Notation Reference: 4.3.1 Line breaking, so let me see what it would take to get this implemented.
In the mean time, you could always download the .ly file (enable in the settings), and then add the \break command and compile the tab yourself.