Considering a second PhD, this time in statistics. Will any professors be interested in working with me?
As most of the comments already say, doing a second PhD is probably not a good use of your time and not very helpful. From an industry perspective you have a math PhD, that means you are very smart and can learn anything, especially any maths very quickly. Learning some statistics or machine learning can be very helpful for an industry career but there is no need to get a formal degree in it. You can state in job applications that you have a math PhD and that you know statistics. Even if the statistics is entirely self taught in the real industry world this is equivalent to a PhD in statistics.