In regards to mushroom cultivation, I think the biggest shift for the griffins would be not so much finding which are good to eat but how to farm them. Assuming that MLP griffins are omnivores (though no doubt preferring meat) and that the setting is medieval, mushrooms would be part of the normal diet.
Kept in the dark and fed on...
While King Golden-Feather made sure to limit the amount of time Archimedes was allowed to present his research findings (to retain his and now his wife's sanity/not put the entire court asleep) in council, that just meant the under-sized academic had gotten very good at delivering large amount of information quickly.
"...still examining other potential sources, but currently we have finalized the farm design and completed test growth run of both Portobeako and Ovumtreatus fungi and can...."
There were also running bets among the councilors on the longest period of time he could continue talking on a subject before he had to inhale. Ravenburg had been making a mint off it.
"All this is....very nice, very through, councilor Archimedes." Interrupted Claus Rosewing, apparently trying to hide a headache from the sheer information overload that the researcher had been pouring out. "But how can any of this improve Griffonia? You've demonstrated that you can grow rot. What more?"
This blunt statement actually made the academic stop for a moment with a rather odd expression on his face. It seemed like he considered Rosewing to be saying the rough equivalent of 'what is the point of the written word' or something equally nonsensical.
"My good griffin, we eat them of course. As clearly outlined in my treatise 'Common Agaricomycetes species of Griff-' "
"On which I must remind you Archimedes, it is highly likely that none of the griffins present have ever seen this treatise, let alone read in full." interjected the king, bringing up an oft-repeated point. While Archimedes was one of (if not the) greatest minds in Griffin lands, he constantly overestimated how popular his various publications actually were among the laybirds.
"I-never-well, of course your majesty. If everyone may recall the hearty soup the kitchens served to us earlier today?" Seeing the nods he continued. "The nut-like flavor along with the strips of 'meat' present were in fact Ovumtreatus used in the recipe.
Though uneducated griffins call them tree oysters. The two species I have grown have often been served as part of our meals, it is just until now they have been semi-rare additions gathered by claw from the wild."
Rosehip began to look more interested as he quickly flipped through his notes. "...So that's what you were up to. And I know for a fact that herd beasts will eat some of those things and others are used for treatments along with herbs. You said your 'farm' can produce mushrooms all year round?"
Archimedes puffed up his (admittedly small) chest in mild indignation. "Of course! Who do you take me for? While we are still ironing out small issues with growing the less commonly used species, producing food and animal fodder is child's play."
"Good. Meet me after the meeting so we can go over the details." As he said this, Rosehip turn to the king with a wide grin on his beak (and Garrick would swear he saw dancing gold coins in his advisor's eyes). "I'll have a report with the costs and benefits of building Archimedes's new creation written up for you by tomorrow, your Majesty."
AN: The two mushrooms Archimedes grew were the MLP versions (named by griffins here) of
Pleurotus ostreatus (oyster) and the
Pleurotus ostreatus (common/portobello). Both of these are dead simple to cultivate as long as you get the growing medium right (pasturized/cooked straw, the right logs etc). A constant and assured supply of fresh (albeit limited in type) foodstuffs during winter? That is
huge in a medieval society.
