I have successfully fished on five characters at the same time without click broadcasting, just manually mousing around the windows and clicking the bobbers myself, having the characters enough spread out to only have one bobber on each screen so I know where to click.
Managed to fairly often catch on all 5, but this was with simultaneous initiation of the cast on all 5. If using an addon that makes you recast from the mouseclick when you click the bobber, it should be very possible to keep catching on all 5.