If it takes 10 people and six hours to accomplish the release of even the smallest of features, then it sounds like there's a bug with your "ship fast" feature and the team should invest some or all of its resources in fixing that. You probably can't do it over night, but you gotta chip away at it over time at the very least.
If you are looking for justification backed up by real world numbers, I highly recommend the book "Accelerate" by Nicole Forsgren, et.al.
Have you considered giving it as a gift to your peers and leadership? I really think it's a great read and resource for anyone trying to sell organizational change.
I wonder if any of those "automation needs" could be turned into startup ideas?
I actually tried a startup in the monitoring space, but sadly failed (it was great fun losing $100k or so, tho... well worth the experience!). But the automation needs problem is more a consultancy thing than a product thing. There are lots of products. Teams buy them, with the best of intentions. Lots of management wants to believe they can buy their way out of the hard problems of not having any discipline. Sigh.