Solution or Workaround
If a coverage is projected after running TIGERTOOL, why do the IDs get scrambled?
Run IDEDIT on the cover1 with the poly option. For example, if the coverage created was county1, then IDEDIT would be run as follows:
idedit county1 poly
Re-project the coverage after running IDEDIT on the cover1 created by TIGERTOOL.
Only cover1 is affected. IDEDIT does not have to be run on cover2 or cover3.