IMHO.... Mr. Diehl clearly explained the matter.
"To be conservative with the inherent uncertainty, most engineers would not model flexibility of the pump housing. I know that standards such as API 610 indicate casing deflection related to allowable load and you can turn that into a stiffness but, in my opinion, it is not good practice.".
You can see that there is a way to model the "stiffness" based on API 610 and there is an advice/opinion to follow "good practice".
I guess we don't need to convince you about topics as "over-design", reasonably "conservative", "my cost will increase", "good practice"; giving you our opinion it's all we can do.
You still have the freedom to experiment your ideas if your Client agrees with you.