Butterflies is larger tree at 25FT with brilliant canary yellow blooms. I have found this tree blooms at a later age than some of the magnolias and you must be patient. Yellowbird is slightly smaller with a deep yellow bloom. Elizabeth is a creamy yellow bloom on a vase-shaped tree of 18-20 ft most of the time. The blooms are very large like a saucer mag. You did not mention what zone you are in as most of these trees are safe in zone 5 or higher. There are many places on the internet that sell them but I would try your local nursery first to save the plant from damaging shipping problems. It is also getting late in the spring to ship plants that are leafed out with the heat that is happening right now.

Too new on the market for anyone to have photos of older trees. Even the original seedling probably isn't finished developing (the final size of a tree occurs when it goes into a decline or blows over). 'Butterflies' seems to have been a hit in the northeast, where it apparently tends to flower well ahead of the leaves. Trees offered at Home Depot could be anything, similarly loose-with-labeling Lowe's had two different variety cards on the same block of a single yellow magnolia cultivar near here this spring. Last year a nearby Home Depot had some sweetbay magnolia labeled 'Elizabeth'. I've been growing 'Yellow Bird' for awhile (it was acquired as 'Butterflies' from a local garden center). It took me a bit of time to figure out it was the one instead of the other. It does have a tendency to flower after the leaves have come out far enough to obscure the blooms. Much (most?) of the point of this introduction was the large size of the flowers, however only one comparatively prime specimen I have seen in this area had big flowers in enough abundance at one time to be impressive.

Move it now - it is the best time to dig and replant - make sure to mulch the soil around the plant so it doesn't heave out of the ground over the winter,

Yes, probably a reaction to not spending energy blooming so much in the spring. Given your observation of sporadic summer bloom (which is common on many magnolias), I don't find it such an eye-popping anomaly, but certainly not the usual case. If all those fuzzy flower buds bloom now, will the tree have the time (or the want) to make new flower buds for next spring? Doubtful. So then I would suspect that it will take one more season of weirdness to get the bloom schedule back on track. More probable though, is that most of the fuzzy buds will stay closed through the winter, and you'll be good to go.