I have to admit I was a bit surprised myself that RTMP is still alive and well. After the internet bust of 2002, Adobe (and the rest of the industry) focused on one-way, broadcast media. Today RTMP is the dominant protocol for live streaming (still used for YouTube, Facebook, Twitch, etc.) In addition to all the companies actively using Adobe Media Server in production, there are a lot of interesting applications for this tech that are growth markets today.
Steven -- I applaud your team's approach. From my two and a half years in government I have rarely run into projects like you describe. We have lots of legacy systems, typically built without automated tests. Often a vendor is hired to build a "complete" piece of software, then given a meager budget to "maintain" it.
I spent over 20 years in the software industry and I've never seen anyone describe software as in "maintenance" except when staffed by a skeleton crew who does not do user research or anything forward thinking. That's ok, I guess, in industry, not ok in government when a fixed size market is not a business indicator, but a fact-of-life.
The ideal team is not three "guys" -- diversity of perspective helps creativity and versatility, of course your team should be aligned in values and methodology. Your post is fine as far as it goes, but there is so much more to the ideal team than just three people with different skills.
When I was at Laszlo Systems, we did that to revitalize the business, not to turn it off. It was very effective at spreading the word about our product and simply shifted our business model.
It did take some time to instigate a real community around an established code base -- if I were to do it over again, I have ideas of things we could have done better. It's also easier now, I think, with github and the rise of social networks.
I've spent some time teaching people web development (Ruby, Rails, Javascript) both as a professional trainer and as a volunteer through RailsBridge. I've seen a few motivated individuals go from non-coder to software developer in less than 1 year. Certainly you can get paid jobs writing code sooner, but these folks were doing real development in 6-9 months.
With an engineering background you already have a good foundation in problem-solving. I would recommend learning one language really well first. I like Ruby or Python for beginners. Javascript is very practical, but I agree with the other folks in this thread who compared it to C. It's lack of structure make it a hard first language. Then find a small open source project to get involved with. A lot of open source coders will happily mentor you if you put in the effort to contribute -- you can start by contributing docs and good bug reports. Get started, see if you like it. It's not easy, but it can be done. For me, it has always been fun.