It might help on the toppers, but I’d use a hard stone, like CZ or synthetic corundum, rather than quartz. Not too much, because the toppers will wear quickly. Personally, I wouldn’t use toppers for anything but roughing, and 3K metal bonded laps, in particular, have a reputation for causing problems.
The Lightning Lap should not be broken in with anything other than normal polishing. Once you successfully get past prepolish, you’ll probably find it’s working fine. If you continue to have problems, Marsh is a helpful guy. Look for information on the website, lightninglap.com, first, and contact them if you have more questions.