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I found a couple more ATC fuses to test, and one of them from old stock or a different manufacturer seemed to have a layer of corrosion on the metal. It took a sharp probe to break through and make good contact.
To check, I hooked it up to a constant current power supply (Agilent 6612) set at 0.219A.
That INA117 circuit that DigitalBob pointed out above uses back-to-back parallel diodes for protection of the input, like we have been talking about. What they pulled out of the bag of tricks is that the diodes are the collector-base junction of two 2N3904 transistors. Those junctions will have far lower leakage current than a signal diode like the 1N4148.
signal diodes like the 1N4148 will be fine for your purpose. Is that what you have on hand?