Let me rephrase the issue to see if I understand this correctly.
Problem:
- You have an index that has three different timestamp fields.
 - You want a visualization for each of these three timestamp fields that aggregate data according to the respective field.
 - You want the timepicker at the top of kibana to affect the respective timestamp field in each visualization.
 
Issues:
- The timepicker only affects the field specified as Time-field of the index pattern in kibana.
 
Suggested Solution:
- Create multiple index-patterns in kibana.
a. create an alias for your index per timestamp field in elasticsearch - Build a visualization for each timestamp field using their respective index-patterns
 - Include all three visualizations on a dashboard to have the time picker affect them all according to their respective timestamp fields
 
Let me know if this helps, or if I was working off of any incorrect assumptions.