"...when i (manually) push the mech across the cassette to shift through the gears, it stops on the second-largest cog just kind of by itself, the lower limit screw isn't even touching..."
That really does sound like the mech just won't work with this frame.
Bonkers.
How much space have you got between the outside of the smallest sprocket and the inside of the drop out? Not much I presume.
What hub are you using?
"...when i (manually) push the mech across the cassette to shift through the gears, it stops on the second-largest cog just kind of by itself, the lower limit screw isn't even touching..."
That really does sound like the mech just won't work with this frame.
Bonkers.
How much space have you got between the outside of the smallest sprocket and the inside of the drop out? Not much I presume.
What hub are you using?