I am interested in getting aggregate dollar values for listings/sales on Zillow (for the whole country summed together, for example). Unfortunately, Zillow's data page seems to only show the "ZHVI", an index value, not a total dollar value. Is there any way to get the total dollar value?
To answer your question of whether you can get a number for 'total home value,' the answer is no–at least not easily.
Zillow (somewhat) recently made available a data set similar to what you are searching for. I suspect, however, that they do not want the public to have access to aggregated value because it would showcase the volatility of Zillow home value estimates, i.e. their algorithm-based estimate fluctuates much more than the estimates coming out of research institutions, etc.
Sorry for the dissatisfying answer!