After soaking them and straining the liquid through a coffee filter, the porcinis still left some grit in my dish... Any pointers for preventing this?
It's not perfect, but try swirling the mushrooms a couple of times as the soak to loosen up any gritty bits caught in the nooks and crannies, and then lift them out of the soaking water when they're ready. A quick rinse doesn't hurt. If you want to use the soaking liquid, pour that into a filter-lined strainer.
The coffee filter will clear the soaking liquid but not necessarily the mushrooms themselves. You might have to give them a short second soak.