Second what Dad's said....has the smaller orange one (the invasive one) got a separate latin name?
Just take on board the warning about the invasive nature of it, and it'll do fine in those conditions, but you've read the warning here! Having given that, I manage to contain the clumps, after a fashion, at the end of the season when I clean up the dead growth & remove bulbs as well, or, like now, at the beginning of their growing season, but the soil will still be 'infested' with teeny bulbils.