Well, some microbes will grow in hydroponic systems. The ones that form a direct connection with the roots should be fine. Ones that break down stuff might not do so well.

I'd look into how hydroponic systems handle it. Then buy some mycorrhizae on ebay or something. It can be pricy, but a little goes a long way and you shouldn't need to reapply short of having to disinfect the entire bed.

I would try to get one of the more diverse mixes (they are sold as mycorrhizae but many also have beneficial bacteria).

More diversity means more stability. That being said, if you are doing something with a steady supply of water, you don't really need more than one Glomus species (Intradices and Mossae are the most popular). Others like G. Desertacola can take drought way better, but it's not necessary in a controlled environment.

A diverse range of bacteria is still good because while some fix nitrogen, others eat or poison bad microbes, some brands even have bacteria that poison fungus gnats.

So even though they say good microbes “crowd out ” bad ones, some actually actively kill them.

I'm curious to know why compost isn't liked in a SIP. Does it interfere with the wicking?

I'd also like to know this. My guess is that it has something to do with particle size, but surely if the compost was used sparingly and at the right size it would be beneficial?

I would posit that it does not wick reliably.