The Lollar HB wiring colours should indeed match SD colours, and so line up directly with my diagrams.

Are you certain your mini-toggle is an On/On/On and not an On/Off/On? Either type of On/On/On should give you a single coil in the middle position regardless of type 1/2 wiring (just a different coil with each type), so that suggests you’ve got an On/Off/On instead. Having said that, even an On/Off/On should give you noticeably different series/parallel coil sounds in the up and down positions, so something else may be going on. Are you testing that with just the neck pickup selected on the 4-way?

Can you post some clear photos of your mini-toggle wiring? Hopefully we will be able to see what’s connected where and what should be happening for each switch type.