Is there any reason to not separately ground the DC ductwork, such as
by driving a 6' copper rod in the garden outside the shop and running a
wire to it?

Thanks.

-- Mark

The reason is this won't clear a ground fault. (trip the breaker)
The ground has to be bonded to the center tap of the utility transformer. This
is accomplished in your service panel via the main bonding jumper. A separately
driven rod is required to be bonded to the service grounding system by the NEC.

What they are probably telling you is that some of your branch circuits don't
have grounding conductors in the wiring method. There has not been a
sifgnificant change in the code in reference to grounding the service in close
to a century.
Homes that were built to "GI Bill" or FHA standards after WWII should have a
grounding conductor brought to the box but you still could have 2 prong
receptacles. You can pigtail a ground out to a 3 prong receptacle if this is
true. If the house was built to minimum code it may only have a 2 wire cable
serving the branch circuits. The only fix in that case is to run supplimental
grounding from the panel or to rerun the cable feeding the circuit.