Originally Posted by Therapy

As a Toolmaker by trade, the word of thumb is full strength is achieved by the threads contact at the same depth as the diameter. So a 1/4 inch nut would be 1/4 in depth. For you it's 5/16. After that little appreciable strength is gained assuming the threads are in good condition which yours obviously are.
You state 1/4 inch thread engagement. By looking at your photos it appears as though your prop nuts are on finger tight. Somebody correct me if I am wrong but I usually end up with some crush on the prop when tightened to what I feel is proper torque. Perhaps that will give you the needed engagement for full strength.

My two cents.