The only neutrino interactions we see are the ones coming from neutrinos moving indistinguishably close to the speed of light. Until there’s a revolutionary new technology or experimental technique, this will, however unfortunate it is, continue to be the case.
After reading this article I thought of Cherenkov radiation and the Frank–Tamm formula. I assume it would be possible to predict how much beta radiation would be produced by a given reactor. You could then measure the Cherenkov radiation to know what percentage of the beta radiation was traveling at above 0.75 c. If nearly all the beta radiation produced Cherenkov radiation it would imply that nearly none of the beta radiation was traveling at a speed slower than 0.75 c.
This would help me put the speed of a neutrino in perspective. Should I expect that there are any neutrinos traveling at speeds much slower than the speed of light? Since they rarely interact with other matter I assumed that they would likely retain the same velocity they gained at the time of their creation.
Can we actually create a model that produces neutrinos that have an initial speed which is much less than the speed of light? Do we have a model of a nuclear processes which would produce a neutrino traveling at a velocity that is less than 99.99% the speed of light? Since the neutrino doesn't easily interact with other matter wouldn't it be reasonable to assume that the neutrino simply maintains this initial velocity?