I faced a similiar situation. Initial 5-6 revolutions into the shell felt easy and nice but at some point I started feeling significant resistance. I took it out, regrease the BB and the shell, and try again. This happens for a few times and eventually, little by little, I manage to thread the BB into the shell by hand. I would like to also add that at ...
The part with the red arrow needs to be turned - as Daniel R Hicks has said
righty-loosy instead of righty-tighty
Your bottom bracket appears to be a variation on the Thompson bottom bracket.
The Thompson bottom bracket uses adjustable spindle cones and cups pressed into the bottom bracket shell like the Ashtabula bottom bracket. Unlike the Ashtabula ...
You most likely need to remove the bottom bracket to re-install that piece, even if you had the inner portion with you.
So just remove the bottom bracket and you'll see the backing portion that you're looking for and it'll be easy to see and install.
And to me it looks like some sort of cable guide used to hold your derailleur and brake cables/lines.