The buyer's home inspector has just indicated that "water heater has slight
back draft and poor rate of rise" and buyer requests this to be repaired
prior to closing.

This sounds like "home inspector" BS to me. Checking rate of rise means a lot
of fussy work with measuring containers and thermometers and stopwatches and
takes more time then the HI would like to spend on the job. Ask to see his work
sheet and odds are he won't even have one. The so called back draft is a
another implausible nifty. If you waft a bit of smoke near the heater vent and
it blows back at you, there is a genuine backdraft. If the vent is joined with
a furnace chimney, there should be an adequate draw at all times on both units.
Put some cotton rags in a tin can, light them and let them smolder fo produce
smoke for your testing. Take pictures of test in action for evidnce for the
buyer.
Go down to your box store and get the best priced water heater you are willing
to pay for and slap it in place. Now everybody should be happy, so enjpoy your
closing. HTH

Joe