By the time it is all said and done you will still have a strip to repair where you install the lines. I have installed a lot of pvc sprinkler pipe and the repair work for a very narrow strip say 10 inches wide compared to a 16" strip is not worth mentioning. You can use the 10 or 12 inch buckets with no more of an issue than a smaller bucket imo. Narrow buckets are bad about clogging up compared to wide buckets, I would think a 6 inch bucket would be a pita.
I have also used my subsoil plow to pull in shallow lines with decent success and dug the intersections with the backhoe. Same for a trencher, still need to dig the intersections up. For most jobs I prefer to dig them all with the hoe because it is easier and less work.