After all the feedback I got from this...
https://news.ycombinator.com/item?id=17154355
Someone pointed me to Reinertsen's Principles of Product Development Flow book, which put into numbers and models everything I'd been trying to say (and then some).
It worked great with my team, but I was failing hard at communicating and involving everyone on the business side so I started researching for something that provided the business side, wrapped around his methods. Which drew me to Scaled Agile Framework.
There's a lot in it, but the core of it is simply on a pace of 8-12 week increments, you spend 2 days letting your developers provide you with a plan, estimated based on 2/3 of their actual available time. They make the plan...not management.
The plan is presented to management, management discusses tradeoffs and options, then ultimately management will accept a final plan and the developers provide a confidence level in their ability to deliver the plan that they have set out.
When new requests come in, they are discussed for the next 8-12 week increment so the developers can focus on executing the plan that everyone agreed on.
There's still room left for small things that come up, there are progress check-ins and communications that happen along the way. Risks to the plan are identified and discussed so everyone is aware of them up front. Variability is assumed (up and down) throughout the plan. The only assumed commitment is to the 8-12 week deliverable. Nothing in between is expected to have a guaranteed delivery date.
It leaves little room for surprises and plenty of room for people to work in a reasonable manner. I can't speak highly enough of how effective it is to addressing this problem.