Are you saying 37 inch lbs isnt high enough to get the fastener to work properly?
If used as a fastener to clamp two things to each other using the 7/16 headed bolt, yes, it will come off with a slightest of vibrations. In practical terms, 37 inch-lb is usually used on #2 (or #3) Philips screws. Very rarely a 1/4 drive would be used on a 7/16 headed bolt. If you pick up a generic 1/4 inch socket set, it will not go that high and there is a good practical reason for it. I am not really understanding your application.
Let me see if I can give another analogy. Suppose you had a flat and thin electronic gauge material (aka wafer film with embedded electrodes) which can measure surface pressure. Suppose a washer was made up of that material. Just to make it more fun, assume the washer had built-in wifi which relayed the pressure to your laptop. I can tell you that if you used a 7/16 mm headed bolt and used a torque wrench to tighten up to 37 inch-lb, the pressure displayed on your laptop would be too small to support 1000 lb of dead weight.
Given that you were within 10% of your calculations, that means you are doing right and I am just not understanding your experiment. So getting back to your original question, most torque wrenches are not going to be any better than 10% in terms of accuracy. So grab a cheap HF and calibrate it yourself using weights. That is your best option.