There can be no such evidence because there is no such thing as a "veil of ignorance". You are fully aware of your social status. It seems likely that this knowledge informs your values.
Your status does inform your values, but we differ in values even if we aggressively correct for social status (as well as upbringing, race, and every other factor). This is a 'nurture vs. nature' issue, where Rawls assumed nature was irrelevant, but was incorrect.
That's not what the veil of ignorance is about. It's not supposed to be a reality, but a thought experiment in order to do the relevant moral choices.