yes, that's it. Amazingly, this is a tree I'm quite familiar with - from a distance. They are in flower right now all over East Tennessee. I've just never been close to a budding branch of one. Very invasive pest. Here's what I found on it: Stem. Twigs and branches stout, glossy gray brown and speckled with numerous white dots (lenticels). No terminal bud. Lateral leaf scars raised, circular, and becoming larger, dark, and sunken. Bark light-to-dark gray, roughened, and becoming slightly fissured. Stem pith chambered or hollow and wood white. Leaves. Opposite, heart-shaped and fuzzy hairy on both surfaces, 6 to 12 inches long and 5 to 9 inches wide. Leaves larger on resprouts, 16 to 20 inches across, with extra tips often extending at vein tips. Petioles rough hairy, 2 to 8 inches long. Flowers. April to May. Covered with showy erect panicles of pale-violet flowers before leaves in early spring, tubular with five unequal lobes. Fragrant. Flower buds fuzzy, linear, and becoming ovoid in summer and persistent on erect stalks over winter. Fruit and seeds. June to April. Terminal clusters of pecan-shaped capsules 1 to 2 inches long and 0.6 to 1 inch wide. Pale green in summer turning to tan in winter and eventually black and persistent into spring. Capsules splitting in half during late winter to release tiny winged seeds. Resembles southern catalpa, Catalpa bignonioides Walt., and northern catalpa, C. speciosa (Warder) Warder ex Engelm., which have leaves with sparsely hairy upper surfaces and rough hairy lower surfaces and long slender, persistent beans.

Could it be Helichrysum petiolare?

Firmiana simplex - Chinese Parasol Tree. HTH CHris Here is a link that might be useful: F.simplex

The only one of your considerations I can speak to is the Carissa holly, which I've had about 8 years on the north side of my house. The are about 3 feet high and I've not had to shear or shorten - I just prune errant limbs when necessary, or the ones on the shade to help thicken them up. They do get as wide as tall (maybe even a little wider than tall) and the ones in more sun are a bit fuller and denser than the ones in more shade. They are a pretty shade of green - new growth is a bit coppery purple, but not for long. No pest or disease issues. I've been really pleased with them. The leaves are bolder than, say the dwarf yaupon, so I think a much prettier holly. I recommend the Carissa.