Make an AmSnag search for each leg of the trip, spacing their "Start" dates by the number of days to complete the previous leg. Then either print, photoshop or cut and paste/tape the results leaving only the dates and fares with little space between them. Then arrange them side by side with the date sequences aligned horizontally. Finally, look for the horizontal row with the cheapest total fare.
Here's an example showing one way to do it using FastStone:
It shows the least expensive date to start this particular trip with no layovers anywhere is on 04/08/19 at $1422. Any other start date from CHI will be a bit more expensive. There may be better ways to do this sort of thing, but this is how I do it.