since filebot/amc is really just a cmdline tool you can probably make it work with any software that can run external programs, or just call it every once in a while with scheduler or cron.
If you can't call a cmdline tool on finished downloads though that's bad. Alternatively you can use some sort of scheduler but calling filebot on complete would be much better.
Are you sure calling external scripts is not supported? Almost any download tools should allow this since it's easy to implement.