The single most useful tactic for converting to a reputed government role would probably be networking.

I'd recommend joining Linkedin and connecting with the following people. Do this in a genuine way, not in a connection-grabbing kind of way. Only connect with people that you genuinely respect for the following attributes:

1) People that you respect or look up to, even if you don't personally know them.
2) People that have already done what you wish to do (e.g. entrepreneurs that have moved into government).
3) Anyone that you think could help you out. Each connection you make will allow you to browse through more potential other connections that you respect and who could potentially help you.

Each time you ask to make a connection, write a genuine message about why you're interested in connecting, and why you might be interesting/helpful to them. Don't use the generic text.

Also, start going to events / conferences, and if you can, be a speaker / judge at those events (lanyrd.com). You could even start your own group / hackathon / classes which could be focused on applying tech to government / society improvement or something.

In general, the more you become respected in the community and build a network of people that you respect, who also respect you, the more likely you are to get the government job.