I totally understand! The outbound can get pricey. The thing with moving to a vimeo or YouTube is you are giving up some control for the reduced price. They will add ads around your videos. They have rules about how you can display them. I have been in scenarios where I have been shut down by YouTube. So there is that to keep in mind.
However, I have had some good success with vimeo and their pro level accounts but they aren't all cheap. They do have absolutely fantastic api support!
You might also look into reserve instance pricing on cloudfront. They will give you quite discount for the commitment.