Have you tried changing this line
in the PICAXE.INI file in the PIC-Logicator installation directory to this?
It didn't work in the free version but as you have the paid version, it might do for you.
If it doesn't work for you, then move the
PIC-Logicator-V1.exe file from the
Old V1 exe directory to the PIC-Logicator installation directory and that
will support 16FXX PICs.
However I don't think it will work with any programmer other than the BAS800 or the PIC-Logicator branded programmer. The About box for PIC-Logicator V1 says "PIC-Logicator V1 PIC interpreter by Clive Seager" so that implies that it will download an interpreter onto the PIC and you will have similar limitations as are present in really old PICAXEs.