OK, a little experimenting.
If you radically shorten the steep time and try not to breathe in while pouring the tea off the leaves, the floral bouquet is actually not all that strong. Most of it seems to end up as odor during the steeping procedure, after which point it becomes fairly subtle.
The second steeping, with just a bit more time, is even less offensive.
Maybe I need to take a whole second look at hand rolled, green, scented oolongs.