Higher than expected SG

I brewed a farmhouse ale this weekend. A 10 gallon batch in a round cooler with a false bottom. It was not the smoothest brew day. My mash temp was a little low (measured 154-155, tagget temp 158), so I added a half gallon of boiling water to the mash to bring up the temperature. After stirring the mash, I attempted the check the mash temperature and proceded to drop the thermometer into the mash tun. I tried to grab it with some tongs and then tried to gently fish it out with the mash paddle, but ultimately decided to leave it. I figured that as long as it did not break, it would not be a problem. I was not planning on doing a mashout, because there is not enough room in the 10 gal cooler to do a mash out. Long story short, my target SG was 1.044, and I got 1.052 @ 70 degrees. I hit my volumes pretty close maybe a half gallon low. I used the beersmith software for all my volumes and for my target SG. Did I inadvertanty do a multi-step mash? There was about 10 -15 minutes while I waited to boil the water to add to the mash. Any thoughts?

Being a half gallon low on volume would explain half the difference, and I am guessing the rest might be from your grains being a little plumper than the values used for standard calculations. That or a measurement error either from the hydro reading (standard temp) or the exact volume. In any case I think your beer will be in styler guidelines and nearly indistinguishable from the target OG version. You can always add a little water for that matter.