When she was younger, she would straighten and stiffen her arms at her sides and her hands would shake when she was very excited. She still has these excited arm hand motions, but no one seems to make anything of them. They have always made me wonder.
This excitement sounds so much like my son (2.5), who isn't on the spectrum. If I'm a hand talker, he's a body talker. He has to move around quickly when he tells me about new ideas. He has one particularly charming, undulating dance-walk combined with fist pump which he reserves for his best ideas.
His sensory seeking is usually satisfied with heavy work, like pushing around and climbing on a sturdy box or piece of furniture, jumping, running at top speed, wrestling, etc. Someone above mentioned a mini-trampoline, which I think is a terrific idea. A skipping rope is also an inexpesive tool--get a good one with ball bearings. The key to ensuring it's calming and not energizing is to mandate a minimum time of intense work--for my DS, that's 10 minutes. Most mornings we go to the park first thing and run our butts off playing for an hour.
Another hack I have for DS is to feed him foods rich in tryptophan--things like turkey (and other meats), milk, beans, nuts, seeds, mangoes, bananas, etc. Tryptophan is an essential amino acid and precursor to niacin, serotonin, and melatonin--all things needed to calm an excited child and support sleep in sleep-fighters.
