This experience will be a big benefit to you in theatre! One way to share it is to do a skills based resume, instead of the more traditional show based resume. As a hirer, if I have someone who applies who doesn't have as much theatre experience I look for what life skills they have that might make them a good SM. This is more similar to a "corporate" resume, but will give your future employers an idea of what you can do, not just what you have done. (It also works for SM's looking for work in the outside world).
Instead of setting your resume up showing this way (or some variation):
Position Show Theatre Director
Stage Manager X Show Y Theatre Z Director
Try setting it up to show what skills you used at each position, starting with theatre experience and working your way back. Use active verbs (organize, lead, manage, coordinate, etc) that describe your responsibilities and any kind of specific projects you may have worked on.
For example, after you have listed your theatre jobs, you might list for your software engineer position something like this:
Software Engineer, XYZ Software, 1990 - 2008
Managed team of 15 engineers who developed software product for large client. Served as liason between client and programming team. Coordinated deadlines and ensured team was able to meet them. Lead quality control committee. Organized data using ABC computer program to create consistent and accurate paperwork for all goverment filing.
You have to sell yourself, but with as much experience as you have, you will be able to identify what those skills are that translate from your other jobs to SM'ing. Project manager and stage manager are only a small step away from each other, and maturity and a diverse background are a benefit in both.
Follow this section with your education, special skills, (particularly anything that might be helpful in theatre, including computer software you can use) and your references.
As LJH and KMC have mentioned, use your cover letter to help employers understand how your skills transfer, and how your diverse background makes you a better SM than someone without it.
Best of luck!!