Should the thermocouple wires be insulated against a metal shaft
Unlike most "professional" thermocouple signal conditioners the MAX6675 requires that the junction be insulated. The (-) lead is required to be grounded near the chip. 

So you need to insulate both wires from each other (and anything else) all the way to the temperature sensing junction (where they meet) and the junction itself must be electrically insulated from everything else. 

Since electrical insulation generally means thermal insulation that typically results in inferior performance to a grounded junction. Poor coupling at the junction generally means more inaccuracy from heat lost down the wires and poorer dynamic control performance due to the slower response. 

A (relatively expensive) insulated-junction (aka "ungrounded junction") mineral-insulated thermocouple can used to improve the situation. They use crushed ceramic as insulation, which is relatively conductive thermally. Illustration below from this site.