Do you have a picture of your grain crush? Is your bag big enough that the grains are very loose and completely mixed with the grains? Are you doing a full volume mash or are you sparging and if so how? You keep saying there was enough water in, but what actual volumes are you using, and do you have a process for measuring them accurately? As was asked above, are you cooling the sample before measuring?
If you mean that you used 6 kg for 28 liters finished volume and my math is right then the expected 1.053 would be about 78% efficiency. Sounds like you are getting about 65% efficiency which isn't horrible but can probably be improved (of course, these numbers only apply if you are measuring your volumes accurately). I never stir during the actual mash and get 77-78% on my BIAB batches. It doesn't sound like mash temp is the issue - unless your thermometer is not calibrated. What water are you using and do you treat or check pH in any way? I think this is likely way down the list for efficiency problems but I guess possible if you have extreme water.