Here is the solution...
Encode all new videos in H.264 format. The existing Flash player on the site is able to run it no problem, with no modification, even with the .mp4 or.mov extensions.. Since Flash Player v9 it supported mp4.
Slowly start to build up the video library. Hire an intern to convert the existing movies. It may take a while, but no rush. Or you can batch process them in Sorenson or AME.
You can continue to use the same player all the way through, and slowly replace the vids.
Then, when you are ready, you could develop an app that taps into the same database of videos.
I'm based in the LA area, so if you want help, or want to discuss it, shoot me a message. I could consult the entire project for you if you wanted, including developing new players if you want.