IMO no hands on bars certainly a factor but I wonder if the weight shift alone was a big factor. It would be interesting if you could find a friend with gorilla arms to to sit up like that while keeping hands on the bars. I don't think 30 mph is *that* fast, so I won't chastise you.
I have a bike with steep seat tube and short chain stays that is by far my most "squirrelly" bike - I can't ride it 5 feet without hands but haven't had a shimmy in any high speed descents whereas another of my bikes has had that occasional issue which I counter by a knee on top tube and a lighter touch on the bars.
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N = '96 Colnago C40, '04 Wilier Alpe D'Huez, '10 Colnago EPS, '85 Merckx Pro, '89 Merckx Century, '86 Tommasini Professional, '04 Teschner Aero FX Pro, '05 Alan Carbon Cross, '86 De Rosa Professional, '95 Gios Compact Pro, '95 Carrera Zeus, ‘81 Masi Gran Criterium, ‘81 Merckx Pro, ‘89 Cinelli Supercorsa, ‘83 Bianchi Specialissima, ‘VO Randonneur, Ritchey Breakaway Steel, Rivendell Rambouillet, Heron Randonneur, ‘92 Ciöcc Columbus EL