What non invasive methods of estimating Body Time are there?
For circadian rhythm, the gold standard is melatonin secretion (blood or saliva). Also, core body temperature. 

see: Circadian temperature and melatonin rhythms, sleep, and neurobehavioral function in humans living on a 20-h day

James K. Wyatt , Angela Ritz-De Cecco , Charles A. Czeisler , Derk-Jan Dijk
American Journal of Physiology - Regulatory, Integrative and Comparative PhysiologyPublished 1 October 1999Vol. 277no. R1152-R1163