One word of advice is be careful when pushing vendors into areas they don’t feel comfortable with. I’ve had many interactions with overseas cm’s and the issue I run into more often than not is a lack of feedback when they have questions or concerns.
I would advise you to get samples as frequent as possible when trying to push back on methods your counterparts may not be comfortable with. They may agree to your standards but in reality it may never be accomplished or the consistency you want can’t be met with their equipment and skill-sets of their employees.
It varies from vendor to vendor but make sure to ask any questions or concerns you have upfront before you agree on something that can’t be revised.
Also is there any way you could revise the actual design of the product to achieve the same aesthetic? You say you want straight no draft walls on certain areas, is it possible you could divide this into separate parts and accomplish this with an extrusion?