Resembles Shooting Star and Fuji Waterfall but SS/FW have white blooms. I would check these colored ones: Forever & Ever Double, Jogasaki, Izu No Hana and Purple Tiers. Remember that the soil will affect the color so a blue-ish bloom picture could still be the one of your plant (grown in acidic soil).
Each of those seems to have signs of the "cap" -- the ones I saw just have the "shooting stars" but essentially no sign of the cap. Does the cap disappear or appear late? Is it possible that I saw it either before the cap developed or after it disappeared?
Yes, it does disappear in time. The center contains the true flowers and once they are pollinated, they gradually change color and become seed pods if they are fertile. The flowers do not last long on lacecaps because, after pollination, the plant begins to put energy into making seeds. Their flowering season may be measured in just weeks... as opposed to months with mophead hydrangeas.
Right. The flowers get pollinated, turn brown and either fell/disintegrated or become seed pods (if fertile). All the while, the sepals stay on the plant giving the blooms a "lacecaps are not there?!?!" look.
Yes, the cap "gets used up" quite fast, around 2-4 weeks. As soon as the flowers are pollinated, they begin to try to produce seeds (provided they are fertile... many are not) and then the lacecap flowers fall down