Is there any way to tell when, how much, and at what purchase price I made those acquisitions? Any way to tell from the blockchain?
When and how much you acquired could be derived from the blockchain if you can decide whether an incoming transaction was a purchase or not.
The price you paid can only be estimated (i.e. look up the price of BTC at that date).
It is weird that you don't see any records on coinbase. Did you maybe use another account? Or a different exchange?