Do whatever you can. Documentation, packaging, training, whatever
Consider even just small steps... e.g. posting small examples of using FOSS can help a lot. I use my blog to help NOAA accomplish its mission indirectly. One instance is how to use QGIS to read data directly from a PostGIS database:
Now, how do I convince the NOAA IT folks that QGIS should be on more peoples machines?
$ cygrunsrv -I cron -p
$ net start cron
Or... install some linux distro and get the real thing
I've had a similar question for Hydrographic Offices in various countries that have to produce Coast Pilot/Sailing Directions documents. Except in their case, this is a document that has 100+ years of revisions and is looking to 100 more years. How do we get them into a process where they can track all the changes and reference where material was submitted from?
I tried to think through some of the options for this kind of stuff here:
Sendmail may be safely run set-user-id to root. -- Eric Allman, "Sendmail Installation Guide"