I had similar issues.
I have a Pico style false bottom installed in keggle with diptube. It takes 2.5 gallons of liquid to reach the false bottom.
I also use a constant recirc. mash system and fly sparge.
Started off around 60% efficiency and changed the following to now achieve around 76-78%.
1) Crush grain myself to a bit finer than LHBS's
2) Thicken my mash to no greater than 1 qt/pound of grain. This lets me add about a gallon more to my sparge water volume. (I was at 1.5 qt/# ratio before changing to ~1 qt/#)
Say I have 10 pounds of grain for my recipe, my mash water will be 10 quarts of water, plus the 2.5 gallons it takes me to reach the false bottom. So Ill be recirculating a total of 5 gallons of "mash" water, but only 2.5 gallons of water is in contact with the grain.....
3) Sparge slllloooooooooowwwww, very slow! With the smaller volume of sparge water we are able to use, its helped me to sparge as slow as I possibly can. I heat my sparge water to about 172-174 to account for some heat loss in tubing/transfer. Prior to sparge I raise mash temp to 168 and hold for 10 mins.
My average sparge volume is 4 gallons and I try to stretch that 4 gallons over at least 25 mins. with the goal being 10 mins for each gallon of sparge water.
This has helped me reach and exceed my efficiency target the last 2 batches.
Also, take a look to make sure that you aren't over calculating how much wort loss your system "produces." Even a half gallon of wort left behind can dock you a few percentage points.
Hope this helps you somewhat!