Is there a way of stopping the tape out warning in the viewfinder when using the MRC1K - other than by inserting a tape of course. I'm satisfied operating the MRC1K alone but would like to remove the flashing yellow icon in the viewfinder.

Depends on the cam. If you have EXT REC CTRL (Z7, Z5, etc) then if you set it to EXT ONLY the tape icon won't flash. At least according to page 88 of the Z5 manual. The Z1 does not appear to have an EXT ONLY setting and does not mention this.