From a chemistry standpoint, multiple washes is more efficient for total KL extraction. In the first wash, you get the small particles added, so it's a matter of KL saturation of the water + the small particles containing KLs. The second wash is where the extraction efficiency starts coming into play. Often you extract the easily accessible KLs in the 2nd wash, you need to go through more effort for further extraction, but you also have considerably less root matter available too. Heating the root powder near boiling and mashing longer helps extract more for the 3rd or 4th washes, but sometimes I'll add micronized kava to the 3rd and 4th washes to bring up the strength of them. I don't add the micronized kava to the extraction container, but rather the cup I drink out of. If you add more kava to the extraction container, you lessening the extraction efficiency of the later washes.
I also have a sonicator I've used many times. It helps, but its efficiency is less than what I was hoping. To release more KLs from deeper inside the root particles, you can use/all any of the following techniques: sonication, mashing, or freeze thaw, but freeze thaw is the slowest and least effective of these.