Igloo cooler for 10 gal batches- too small?

I posted this on another thread, but I'd like to get more input and more in depth with what I'm trying to do.

I've been attempting to do 11 gallon batches in a 10 gallon igloo cooler. For an IPA that I'm about to do, it calls for 31 lbs or grain. If I calculate my strike water at 1.25 qt per pound, I come up with 9.69 Gallons needed. That doesn't leave much room in the cooler for the grain. I did a brown ale recently and ran into the same thing. I just filled my cooler with strike water as much as I could. I felt the batch tasted a bit thin as a finished product. I also batch sparge. Anyone run into this problem and have a solution?

The recipe mentioned above is Jami's IPA recipe. I planned to make a double batch of it. I've been successful with hitting my OG through batch sparging and my total volume to get 11 gallons in my fermenters is 12.5 gallons pre-boil. Does it matter as much to have a water ratio as mentioned above or could I just throw in half of my expected boil volume? So use 6.25 gallons of water for the mash vs trying to calculate 1.25 qt per pound.

That cooler is maxed out at around 23 lbs of grain.

I have found that 26 lbs with a thicker mash works. I go 1.1qts per lb. For bigger beers mash a little warmer and then compensate with sugar.

Yeah, 25 lbs is the max that I get with my cooler at 1.25 q/lb. If the recipe calls for more than that, I throw in a little extract.

From Bobby_M