When a superseding indictment adds charges arising out the same act, transaction or common scheme, the Sixth Amendment speedy trial clock for the added charges still runs from the initial indictment.
The protections of the Sixth Amendment are generically distinct from Due Process and double jeopardy, and differ from the statutory protections offered under the Speedy Trial Act; the protection therefore arises directly from the Sixth Amendment.
http://media.ca1.uscourts.gov/pdf.opinions/17-1961P-01A.pdf
Since 2011. An occasional commonplacing of the U.S. Circuit Courts of Appeal.
Neither an authoritative statement of the law nor legal advice. Quick work.