You don't need another hunt group, at least not according to the information you have provided...
In the main hunt group, add an extension list with the phones you want to ring on the third ring, and then add it as the second position in the hunt group members. In Hunt Group Timers, set the No Answer Advance to about 15 seconds (approx 3 rings, adjust as necessary) and pay attention to the Recall timer. Go back to the Members and add the new extension list as many times as multiples of the No Answer Advance timer is to Recall.
For example, Extension List P0001 is the first group, and Extension List P0002 is the second group of phones to ring. You want the first group to ring 12 seconds, then ring the rest 40 seconds before going to the recall point.... Set No Answer Advance Timer to 12 and Recall Timer to 40
In Members add P0001, P0002, P0002, P0002, P0002
Should be exactly what you need...