I agree with the CPI being the CPLie. ShadowStats shows this just by using prior CPI formulas. Around 40% of the prices used are "estimates." Hedonic adjustments are a joke. Items are swapped out for other items like the classic replacement of steak with ground beef, or even removed like coffee more recently. Etc.
I don't know if calculating the inflation of the above ground stock is necessary, though. Roughly the same quality of goods should be available today for roughly the same quantity of gold as at any given time in history. I'd be interested to see any data showing otherwise.