Amazon S3 and ffmpeg

So we are setting up a file upload system for our web app. Files will
be uploaded to Amazon S3, and videos need to be converted to ffmpeg.
We have had problems with uploading of large files timing out, and it
was suggested to us to use
for uploading directly to S3. This would fix the timeout, but then
could I use ffmpeg to convert the file once it is on S3? If so, how
would we accomplish this? If not, what would you suggest either for
fixing the timeout issue or for processing video conversion?
Essentially, what would be our best solution? Thanks in advance!

buy ec2
upload directly to s3
then ec2machine(or ferm) download from s3, convert, and upload to s3

traffic between ec2 and s3 free
Best Regards, Dieinzige