Thanks for the responses.
Ok, so to answer some questions/provide more information. The hydrometer reading seems real. My Tilt said .996. I pulled a sample and tested with the old fashioned hydrometer and it said .997. I tried the hydrometer in water and it read an even 1.000. The hydrometer was also agreeing with my refractometer when I pulled samples pre-fermentation, although obviously refractometer won't tell me anything now. Also, I made a witbier since then that gave perfectly normal hydrometer readings. So fairly certain on the gravity? Give or take a couple of gravity points.
No off smells that I can detect. It's pretty damn boozy, but I would expect that with that kind of gravity reading. It's pretty thin, which again I would expect. I have no idea how that evolves over time since I haven't made this style before. Could easily just be green but with a FG that low I'm in totally uncharted waters for me.
Brewday was definitely a little weird. Recipe called for a protein rest at 127F, so I did that. Sacc rest was supposed to be 152 but I missed it by several degrees (forgot to pre-heat tun, oops), so it started at around 147. I pulled a couple of quarts of mash and got it up to around 180 and re-added it, which got my mash temp to 149, which I called good enough and mashed normally. Then when I went to boil, the regulator on my burner broke and would only operate at about 10% power, so it took almost 2 hours to get to a boil. Boiling had to be done under cover because of the low heat, so I was concerned about DMS, but just didn't really have much of a choice. Finished boil, went to aerate and was out of O2 so probably did a poor job of aerating. Then the yeast took a solid day to get going and just would not stop chugging for 3 full weeks. I kept thinking it was going to stop, first at 1.014 (the expected FG), then at 1.008, then at around 1.003, but it just kept going.
So that's the saga. It seems fine but hot and thin. Further thoughts?