As your explanation, I think it is a water hammer or pressure surge because it happen during start up and shut down with fluid in the pipe.
In case of closing control valve to 20-35%. This is not solution.
Where is this control valve, upstream or downstream?. If it is at upstream, it will make high pressure drop and cavitation at pump suction and then vibration will more severe. But if it in discharge line, greater pressure drop at discharge line will consume pump power and may be cause of vibration as well.
How to solve this problem? CII have function "Water Hammer" in dynamic analysis. You can use this function to analysis the piping system. But you should obtain the force at each elbow first and input in CII to check stress analysis. The other calculation program can be checked for you but CII can not. The other supplementary method
1. pipe support should be proper designed to withstand the surge or water hammer load.
2. start up and shut down time should be longer than critical time of piping system
Regard,