Ooops, guess I missed this post when it first was submitted.
Actually 110v is more amps (as voltage lowers amperage increases for the same wattage output). At 110v it is 13.64 amps (14amps for all argument). That 10 amp fuse should be long blown, and it is not properly doing it's job. I suspect you have a faulty fuse.
The specs for that unit show the maximum amp draw is rated for 13 amps. You are overloading the controller running a 1,500 watt element.
Also cut and pasted from their page for the WSD-1204CPH:
4) The power rating is 1450 watts for 120VAC, more than sufficient for the 500 watts required by the Bradley smoker. It will also work for Bradley Smokers that have an additional 500 watts heater installed. If you are going to use it for larger smokers, you need make sure the total power drawn, including the smoker generator control output, should not exceed 1450 Watts at 120V (or 2000 Watts at 240V).
For a 1,500 watt element you need their model WSD-1503CPH which is rated for 1,800 watts (but you already knew that).
Another option since you already have the unit in hand would be to modify it. There is no reason you could not take the output from the PID that switches the heating element and use it to trigger an external SSR which will actually control as big of a load as you need (assuming the SSR & wiring are properly sized). If you are handy at all with electronics or household wiring it would not be a difficult mod.
I believe that model uses a dry contact mechanical relay to switch the load instead of a SSR. Ask Auber Instruments if there is a software option for a low voltage DC output that can trigger a SSR (it should be a programming change you can do if there is). If not, you can still use a dry contact relay to trigger a DC power supply to trigger a SSR for a higher amperage load. The common 25amp Fotek SSR which is sold by Auber and also available on e-bay, etc... will work. If you go with a SSR make sure to properly heat sink the unit as well.
You should be able to do the mod for much less than the shipping cost you quoted, including the 2nd housing for the DC supply if needed.