Tender directed sweep or arc searches are the easiest and most effective. I know where you're coming from with the circle search - they sound like they'd be the fastest but they aren't. I can't remember the last time we did a circle.
Just something else for you to ponder
...it would be better, but you are using comms. right? One could do it on line pull signals, but I'll tell you Pal, I'll only have so much time to train these lads ( I have two former commercial divers, the rest are basic level scuba & most are inactive as sport divers ). IMO, circle searching can be done quite quickly - when your not tethered! And comms., while ideal, would not be necessary.
Another sad reality: my dept. will never pay for ILS to come up here; likely the best I'll be able to do is to go to them & and take whatever training I'll need to take back to the group.
So my friend - "a pondering I will go!"
DSD