Grossly over sized system trying to pump through drinking straws, per chance? There be holes in them there ducts?
3 tons feels too big for a brand new energy star insulated house with very little glazing exposed. The HERS raters I communicate with on another site instantly suspect shoddy engineering when the spec calls for more than one ton per 1000 sf.
Something is definitely wrong, that thing should recover in 15 minutes. And with long run cycles you report, AND A DEHUMIDIFIER RUNNING, the RH is way high.