Is somebody aware of ffmpeg as a statically linkable library so that instead of shelling out to ffmpeg, the black magic happens within Perl?

I must admit I'm a little bemused by your desire to replace a well tried and tested executable with all the built-in logic to perform the gif-to-mpeg conversion -- things like a switches: to ensure the frame sizes are powers of two; adjust the bitrate and quality; choose the frequency of keyframes et al; -- in favour of a library that would probably require you re-create all that logic yourself.

The ability to easily shell out to well tried and tested tools is one of Perl's great assets as far as I'm concerned.