Update!
Unfortunately, one other immature pseudobulb that looked sickly when I repotted the plant didn't make it. That stinks
However, the two growths I thought were spikes are actually two immature pseudobulbs, and the new growth pictured above is maturing quickly into a pseudobulb as well. All three new growths are putting out roots that are MUCH fatter and happier-looking than the other roots on the plants. I guess three pseudobulbs will make up for the two I lost while figuring out how to grow it, right??
