What you describe is a theoretical possibility but a practical impossibility, as the Government found out when it tried to prosecute Oliver North after he had given immunized testimony; it's impossible to show that the trial wasn't tainted by the immunized testimony. It can be done here only because this defendant was already tried and convicted before he was given immunity.
I find your faith in the integrity of the US legal system charming.
Bless your hearts.
(see also “use and derivative use” immunity)