mpeck -
Ill remind you the point of this post was to determine the minimum speed. based on your description above, after numerous posts and discussions, it is clear that the minimum RPM is not the question, it is the minimum flow of the pump. This entirely has to do with flow and NOT cavitation.
in essence, aside from the info. recommending to contact the pump vendor and reducing the impeller diameter, all posts are off topic because of a poor initial description.
The min. flow is based on the pump design (recircluation of fluid, bearing vibration, etc.) from the OEM. Youll also notice the the min. flow isnt listed on the curve you provided us - these are the pitfalls of going with tier II/III pump companies.
Best advice - contact the OEM - first tell them the pump size, speed, and current impeller trim, the head and flow currently and the head and flow desired - ask them "what is the min. flow for this pump operating at a reduced speed to achieve the requested head?"