The single biggest factor in mash efficiency is the quality of the crush. If you can't get the water to the middle of the particles and leach the sugars back out in the time you mash, your efficiency will suffer. Since you are doing a conventional mash tun, you have limitations on just how fine a crush you can deal with. If you can't drain the tun because the grains were milled too find and won't form a filter bed, your efficiency will be plenty high but the headache from trying to unstick it won't make it worthwhile.
If you have your own crusher you can try setting it a little closer. If you depend on someone else to do the crush, you are at their mercy.