OK, well it's a (very) long shot but here goes...

Has there been any consideration given to this being an orthostatic type reaction? the otolith organs stimulate the autonomic nervous system to upregulate when we go from lying to sitting to help prevent our blood pressure going through the floor (by activating postural muscles). If the sensors aren't working properly through neurological dysfunction - the small vessel disease - then the movement from lying to sitting might (and this is a hazy theory at best) trigger an overzealous response and instigating a strong extension reflex. - do the patients arms extend and neck extend at the same time as the leg extension?

perhaps try sitting the patient in increments by raising the bed head 10 degrees... guage the response, then the next day try 20 degrees and see... etc etc. you might find a happy place part way to get the patient accustomed to for a while before going all the way to full sitting.... or perhaps try leaving the patient lying but lift head forwards (up off the bed if their neck allows sufficient movement) and see if the same "panic" response is elicited with the body remaining essentially flat but head upright.

Other option is perhaps to see if it's a sensory organisation issue and see if the same response occurs while the patient's eyes are closed/covered so they receive less sensory input which may confuse the brain less....????

That's the extent of my guesswork for today!

msk101