A while back when I was throwing 16s, mine was hooking a bit earlier than I like so I took it to P4000 grit + polish. AFraid that doesn't help you.
I'd suggest trying sanding it either with a green nylon pad (600 grit CAMi/P1200 grit FEAP) or a 1000 grit Abralon/Siaair pad (P1000 grit FEPA or 550 grit CAMI) and then applying a light coat of Lanemasters Factory Finish polish. This should make it read the midlane sooner.
Alternatively, take the cover up to 4000 grit Abralon/Siaair (P4000 grit FEPA). (Use P1000 grit pad, then P2000 grit pad, then P4000 grit pad). Leave the surface matte. If this surface is at all shiny, you either used a P4000 pad that was used up or you applied too much pressure. It should have a matte, non-shiny appearance.
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"None are so blind as those who will not see."