A poor crush is one possibility, but you can make up for that to a certain extent by mashing thicker or mashing longer. Both of these will change the flavor profile of the beer. Mashing thicker should produce a more dextrinous wort, and mashing longer will produce fewer dextrines.
If you can borrow a mill that is known to give good results, I think that would be a much better place to start rather than messing with the mash.
Other possible mash problems could be caused by poor water chemistry (insufficient calcium, or bad pH) The pH could be treated by 5.2 buffer from 5 star chemicals, but this won't help if you pH is good to start with. Lack of calcium could be treated with calcium carbonate (raises pH) or calcium sulphate (lowers pH). If you are not using brewing salts, a water analysis should give you a good idea of the amount of calcium in the water. Your water supplier can probably tell you how much calcium is in the water See How to Brew - By John Palmer - Using Salts for Brewing Water Adjustment for some good information on water treatment.
It has been my experience that the lautering process is much more likely to result in poor efficiency.
I brew 5g batches using a round cooler with false bottom, and a sparge arm to fly sparge. (A junior version of what you have.) I collect about 6.75g from the sparge.
I usually take about 60 minutes to sparge a beer with a gravity of 1.045, and this extends to 90 minutes for a beer with a gravity of 1.070. I would guesstimate that your times should be increased by about 50% to account for the larger volume.
I increased my efficiency by 10% simply by adding a mash out at the end of the mash. In my case, I added about 1g near boiling water. In your case, it would need about 2g. Before I did this, I measured the grain bed temperature during the sparge. It never got above 155F! After the mash out, the entire sparge was conducted in the upper 160's. I was also surprised by how much my sparge water cooled during the transfer from the HLT to the grain bed. I now heat by sparge water to 185F, add it to an unheated HLT (a 5g cooler) which drops the temperature down to 180 - 182, and the water exiting the sparge arm has dropped to less than 170.
In addition to monitoring the grain bed temperature during the sparge, there is one further test that is worthwhile when the sparge is complete. After stopping the collection, add another 1 - 2 gallons sparge water to the MLT, and then stir really well. This will dissolve any remaining sugars that have not been collected in the MLT.
After waiting about 10 minutes, collect enough wort from the MLT to perform another gravity check. When it has cooled, check the gravity. If it has risen at all, then you have channeling problems, probably caused by sparging too fast. When I did this test, the gravity after adding an extra gallon water was well under 1.010
Hope this helps