I have a slightly different view on small/mid-size companies: it's not exactly that they can't afford an in-house math/stats person, but rather that there isn't

I have a slightly different view on small/mid-size companies: it's not exactly that they can't afford an in-house math/stats person, but rather that there isn't enough work to occupy one full time (i.e. it's not a budget problem but an ROI problem). So if they confuse themselves into thinking they should hire one full time they necessarily need to offer below-market rates to get positive ROI. It's much more common for small to mid-size companies to have 1-2 projects per year that could benefit from some mathematical analysis, and the ones I've worked with will happily pay for project work where the ROI is clear. And in those cases I think you can fairly negotiate an attractive rate.