My guess is it's a calibration issue -- both calibration of your hydrometer and your mash thermometer. When's the last time you've calibrated each? If for example your hydrometer is reading 4 points low in plain water (0.996) then you would need to add 4 points to all of your hydrometer readings, in which case you might actually have OG 1.097 and FG 1.013, which would give a more reasonable attenuation of 86%. And if your mash thermometer reads a little high and you've actually mashed say 4 degrees cooler than you thought, this could also increase attenuation i.e., lower FG. Have you calibrated your mash thermometer in boiling water adjusted for your elevation? For example here in Wisconsin we are 600 feet above sea level so water actually boils at 211 F instead of 212 F. For every ~500 feet elevation, boiling point is about a degree lower. So then if my thermometer reads for example 216 F in boiling water, I know it's high not just by 4 F but by 5 F here, and then when I think I'm mashing at 152 F, I might actually be mashing at 147 F.
These are just examples. But look into it.
P.S. Mashing out or lack thereof is NOT a significant player IMO.