I wonder whether there is a SendMessage call available to disable the message beep(?)
Yeah. I doubt it, though. It's probably processing the WM_CHAR event (as a result of you pressing TAB) and then calling MessageBeep.
WM_CHAR
Writes a character to the single-line edit control and sends the EN_UPDATE and EN_CHANGE notification messages to the parent window. Writes a character to the multiline edit control. Handles the accelerator keys for standard functions, such as CTRL+C for copying and CTRL+V for pasting. In multiline edit controls, also processes TAB, and CTRL+TAB keystrokes to move among the controls in a dialog box and to insert tabs into multiline edit controls. Uses the MessageBeep function for illegal characters.
I don't think you could intercept this, because the hotkey event invariably occurs after the Blitz engine/Windows processes the WM_CHAR event. It would have to be changed (if possible) when the gui is made available to the user, which would probably have some unwanted side effects.
My fingers are still crossed, though.