The problem is "value" comes through a subjective lens. Different employers value a given work product differently. The OP's big-co employer is likely to value process and documentation.
In this start-up environment, speed is also relevant. Make lots of value quickly.
edw519's 90 pitch works largely because he presents himself in a manner for his customer to clearly see the value he would create. He spelled it out.
Its less about talking about yourself and more about talking about them.
The key thing the OP needs to do (and should have been doing) is networking (outside of work). As others have pointed out, with that much experience, you also should have a network of folks to reach out to.
It can take a long time to build a network. Fortunately, there are tons of opportunities in tech to do so. I'd imagine one of the best paths might be to fine a moderately significant trending (but not trendy) open source project and start getting involved in the community (in whatever way the community needs (maybe not coding initially)).
Learn the code base inside and out. Read the forums, discuss things with people. Create value! Find something needed and do it!
You'll meet people (virtually) along the way. Build a public reputation (very important), and maybe find a job. At least you'll be able to reference your relevant skill in said open source project. You'll then be an older developer, but with very relevant job skills to someone out there.