Austrian Economics and Interval Value Scales

I've been reading about Austrian economics, and how it differs from mainstream neoclassical economics. My understanding is that the Austrian economist's main criticism of neoclassical economics is that neoclassical economists treat value as interval, while one could only objectively claim ordinal preferences; that is, Austrian economists claim individuals only have an ordinal list of preferences, not a continuous interval scale of value. And they're right, you can't objectively claim that value is interval, but if value is ordinal only, then it is very curious that neoclassical economics is useful at all.
If neoclassical economics were totally wrong, then it wouldn't make successful predictions. So the truth must be somewhere between Austrian and neoclassical economics. I would like to suggest that interval value scales may be a useful approximation of actual ordinal preferences. Approximations are widely used in the sciences. For example, in physics, Newton's laws of motion are used all the time to make very accurate predictions even though they are approximations that ignore relativistic effects. When physicists figured that Newton's laws of motion were not entirely correct, they did not throw them out; they simply noted that they are approximations and made sure to note when they are useful and when they are not. This same approach could be used in bridging the gap between Austrian and neoclassical economics. If it could be shown experimentally that for many goods, the value scales of individuals are near interval then much of neoclassical economics would be validated. I haven't been able to come up with an experiment that would resolve this question, but I don't see any reason why it should be impossible.
I find it curious that nowhere in my readings have I found anyone who discusses the possibility.