I manufacture packaging equipment so if you have equipment / filling / capping / labeling questions, please pm or e-mail me and we can talk about it. Even if you have questions about another manufacturer or a co-packer.
Filling 144 bottles per batch is a really low volume that probably doesn't cover equipment cost and I think you'd be hard pressed to find a co-packer that would be willing to fill that small of a batch - at least at a reasonable price.
You would have to look into local Health Department Codes to determine if you could fill "by hand" or a non measured and non machine fill for retail sale - even if you are making and filling the sauce in a commercial kitchen.
If it is possible to hand fill, then you can find a kettle with a spigot on the bottom. I'll assume you will have to hot pack your sauce (above 180F) so the containers will get hot in your hands and there will be a splash hazard from the spigot too. Not fun but doable - I've seen sauce filled in just about every environment - legal or not.
Meat, Inc. De Profundis