I've had a lot of trouble with fungus gnats when it comes to seedling trays that I keep inside, and there are only 3 methods I've found that actually get rid of them:

1. let the soil dry out until you kill off their entire cycle (which is too long of a drought for my young cacti)
2. move the tray outside (also not an option)
3. remove the organic components of the soil

I've used inorganic mixes for other plants before, but I don't want to throw off a needed balance for the loph by taking out the compost I would normally use.

So far this is my intended mix:
4 parts perlite
1 part lime
w/ application of fish emulsion for fertilizer

My thinking on this is that yes my soil will have less water retention which will mean more frequent watering and yes it will also retain less fertilizer, but this can be compensated as well. I'm unsure about how the seeds will set on top of the course/large perlite, maybe i could add an inch of crushed perlite to the top of the mix?

All the mixes I've read about for L. Williamsii include soil... Have you considered sterilizing your soil and adding a couple parts of it in that mix?

The problem is that I can eventually get rid of them, but after time they find their way back into the house (be it the door being opened, riding on groceries, ect.). Sterilizing would work to make sure they weren't in the soil to begin with, but it doesn't stop them from making a home in the soil if they happen to get back into the house.

do you mean limestone- or lime?
if even partially available lime- 1:4 is probably Waay to much

limestone.

I know the little buggers well and I know how fond they are of indoor warm, moist plant pots. Just leaving my 0,02.

I would still use part organic, sterilized soil in germination for better results and isolate the pots/tray in a large ziplock bag or equivalent, which you can open periodically for gas exchange in case you don't want to poke tiny needle holes. The need for moist soil, particularly in the surface, will decrease as the cacti go past the seedling stage and by then you can completely expose them. Water from below to keep the surface drier, and cover the soil with an inch of small grit or sand so any adventurous gnat cannot lay eggs easily.

Gnat problems are well prevented monitoring the soil, and applying some beneficial nematodes (i.e. Nemasys) in case of doubt. Gnats feed on fungus and algae, and these can still develop in perlite over time, as the roots themselves provide organic matter.

But if you still decide to go the perlite-only route, consider at least adding some sterile coarse sand to make the soil mix heavier and more consistent.