I was in a similar position: I worked in a technical, mathematically sophisticated but very specialized job for ten years out of undergraduate before applying to an applied math PhD program. I am currently in my first year of this program.

In addition to taking the subject GRE, I got letters of recommendation from supervisors at various technical positions I had been in. I was lucky in that my employer is very well known in the academic circles in my area, so I think that the math department believed that the letters of recommendations knew what they were talking about, even if they didn't understand them exactly.

So, it might be helpful if you can get letters of recommendation from some colleagues who are at least in touch with academic circles. Depending on the size of your employer and/or the school, this might be easier or harder.