There's your problem: you have a human in the loop. You can't do CD with humans in the loop. The whole point of CD is to rely 100% on your automated tests. Your PM is part of the problem, not the solution. If he insists on signing off manually on everything before it ships that means there's a lack of trust for people to do the right things. That's bad; call it out.
When it comes to acceptance testing, your PM should be doing that in production and keep on insisting on incremental improvements until the feature can be signed off on. Likewise, the pressure should be on developers to not merge things that aren't production ready and to keep production functioning correctly. If unacceptable/poorly tested changes are landing in production regularly, that means your PM messed up planning the feature or the team messed up building the feature. Either way, that needs to be fixed if that happens regularly but not by crippling CD. If that happens, you have a competence problem, not a process problem.
The longer PMs drag their heels, the more expensive deployments get. The cost of a deployment grows exponential to the size of the delta. The price of shipping a 1 line change: almost zero. The price of shipping a delta that touches double digit percentages of your code base: weeks of testing; integration headaches; haggling; over time, etc. It gets ugly very quickly. Add to that the cost of not having features that were ready to go weeks ago adding to your revenue. The economics here are brutal. Not doing CD is very expensive. You end up wasting lots of time and money.
The opposite is also true, the cost of fixing issues resulting from small deltas is very low. So, shipping lots of small things ASAP lowers costs by decreasing testing effort, maximizing time to market, and decreasing the cost of defect fixing.
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