Are you the guy from Systm? Or just have his picture as an avatar?
Um, neither. Maybe everyone looks the same when reduced to avatar-size? (yes, it's actually me. I think this is a big improvement over my last avatar pic, where someone said I looked like someone's grandma!)
maybe using the pinless package
It would be very tight, but it might JUST work. It looks like the pins are laid out somewhat more conveniently that I expected. OTOH, there's also that exposed pad...
both 5mm wide, while the socket pins are ~8.2mm wide
5mm, plus a bit for the pads. Where did you get 8.2mm? Socket pins are 0.3 inches; 7.62mm. But that's center-to-center. Subtract about .35mm for the pin diameter, and .2mm for the pad that the pin needs to solder to, on both sides, and you're left with about .75mm on each side of the tiny package. Very tight...