Gday Mel
I dont think 0.1% resistors will help here, as he wants accuracy to 0.01V.
0.1% resistors are guaranteed to be within that percentage of stated value, hence you can get matched sets, but they do change resistance ever so slightly with temp changes. If this is what is occuring, it wont help. Lowering the measurement baseline using a Vref-, Vref+ type chip, then adding a baseline offset, ie real ground to Vref- will reduce the errors by a factor of 3, but its still like sticking a micrometer onto a wooden ruler using gaffer tape.
Andrew