In real life, I would be less worried about shaft deflection at "run-out" compared to operating at CV. Operating well right of BEP introduces other problems, cavitation, mis-match of flow onto the impeller blade, possibly with pre-rotation, noise and vibration, possible seal damage, bearing overloads etc. You haven't indicated what size pump you are talking about, if it was a 0.5kw unit I wouldn't be concerned in the slightest about operation well right of BEP, on the other hand if it is a 1000kw unit when I would be very concerned.
It is a capital mistake to theorise before one has data. Insensibly one begins to twist facts to suit theories, instead of theories to suit facts. (Sherlock Holmes - A Scandal in Bohemia.)