Add a second checkbox that is checked by default: Join From Beginning (JfB). Quick code in the background to select the other box if you ever try to deselect both.

JfB only checked: Same as regular queue now without Join in Progress (JiP) checked.
JfB and JiP checked: Same as regular queue now with JiP checked.
JiP only checked: New queue type. Only searches for in progress runs.

Done.