"We have to track it down" (or, in an alternative form, "We have to track down the source [of the drug trafficking, of the pollution, etc.]") is about as emphatic as you can get without being redundant.
Per the Collin's Dictionary definition, "track down" already specifies a long and difficult search. Other sources define it similarly, such as the American Heritage Dictionary:
To pursue until found or captured: tracked him down at the pub
and the Merriam-Webster Dictionary:
to search for by following evidence until found // track down the source
Based on the above definitions, I would argue that including "adequately" is redundant; if you don't track something down adequately, you most likely haven't actually tracked it down.
Similarly, "to the original source" is redundant because source itself is typically defined as the origin or the beginning.