You could try "hooking" the message box so that it goes to your own WebPage procedure that would display the message (or log it or whatever). If you have Capesoft's Message Box, you could adapt their Messagebox procedure, or it's not too hard to write your own.
PROP:MessageHook: "A property of the SYSTEM built-in variable that sets the override procedure for the MESSAGE internal Clarion procedure. Equivalent to {PROP:LibHook,6}. Assign the ADDRESS of the overriding procedure, and the runtime library will call the overriding procedure instead of the MESSAGE procedure. Assign zero and the runtime library will once again call its internal procedure. The overriding procedure's prototype must be exactly the same as the MESSAGE procedure. (WRITE-ONLY)"