So, I was skimming back through How to Brew about this. I read that you should stir the mash and check the temp every 15-20min during the hour long rest. I did not do this, I got the mash to the temp I wanted it to be and closed the cooler and forgot about it for an hour basically. Is this just a recommended thing to do and not necessary, or can this improve efficiency?
Stirring might help speed up conversion a little, which could help your efficiency if you are simply stopping the mash too soon, but it is completely unnecessary. Your biggest gain would most likely come from crushing finer (or double-crushing, if you can't adjust the mill). If you're stuck with a coarse crush, mashing longer might help. Probably better still, stepping the mash temperature up to 158-162°F for about 20 minutes after the main mash will improve gelatinization and speed up conversion to get more of those remaining points out.
It appears that you only got about 75% conversion efficiency. If you want to maximize your efficiency, you need to mash until you get 100% conversion. Kai has gone to the trouble to make this table for us, which gives you the gravity that your first runnings should be for a given mash thickness, when you've hit 100% conversion:
However, tschmidlin pointed out a big problem with your process, you left a lot of wort behind and have a big dead space. Particularly in light of your small batch size. With a dip tube, you can reduce your dead space, I have about 1 cup dead space, for example. In addition, you should add only enough sparge water to hit your kettle volume, so that you drain the tun completely.
Reducing your dead space alone could have raised your efficiency by about 5%. Collecting all the second runnings combined with reduced dead space could have raised your efficiency nearly 10%.