Just to clarify, yes an IRI would need 800 hours IFR, however that is for a stand alone IRI rating for someone that does not hold a current FI rating.
For a FI holder to teach IMC and IR it is the removal of the no applied instrument restriction from the FI rating that is required in which case 200 hours IFR is required (or 50 hours recorded as flight as sole reference to instruments under the four to one ruling would also meet the requirement).
To teach single engine CPL only a minimum 200 hours of FI experience is required.