Gage accuracy usig the 10-1 rule will have to be .0004.
Gaging the width of the slot I would use gage pins in .0005 size steps. Gaging the depth of the slot if you want to avoid the extra gage block I would get a reduced diameter spindle and directly measure the thickness from the outside diameter to the flat in the keyway. Measuring the centerline and axial runout of the key will require a specialized gage requiring you to locate on the OD datum and traverse axially down the shaft with an indicator. A custom gage is probably your only option if you want a measument. Alternatively you could install a gaging key and then use a go/no-go gage ring to find out if the part was in or out of tolerance, assuming the keyway can be gaged from the end of the shaft. Size, configuration, and location of measurement(on the machine or off the machine) are considerations. Measurement on the machine will have to address interference with fixturing and clamping devices.
Centerline and runout issues are typically setup issues and could be addressed by using a test indicator from the machine spindle and using the machine to check centerline and runout, measuring the OD of the shaft for parallelism to the axis and then the centrality of the keyway to the OD. I assume you are cutting this keyway with a CNC mill.
I do not know the accuracy of in-spindle probes but the OD of the shaft could be probed by the machine and centerline adjusted to the actual location of the part.
Cost is the real issue. Moving to more accurate gaging from your current process, is the additioanl cost justified? Is the process currently failing? Is there an unhappy customers(in-house or consumer). I would recommend moving away from dial calipers and moving to micrometers to get the hand tool accuracy improved. I am not sure I would recommend the runout or centrality gaging as the problem should only be in the first piece and be tooling dependant.
Good luck on your project.