We have been in contact with an attorney in Rome by email who deals with visa issues and his recommendation is that we resubmit our application with different housing arrangements and the extended stay visa is the correct visa for our situation. We have also learned that there is an appeal process but that can take up to 60 days.
We are moving towards establishing residency where we are now (in Ohio) and submitting our visa application to the Detroit Consulate. Based on the information we can find on the application process with Detroit they have a more streamlined process and a quicker turn-around time. Unfortunately we have not been able to contact them by telephone nor had any response to email to get more detail on some specific questions we have.
There are still many questions we do not have answers to and we do not want to make another misstep like we did with dealing with the Los Angeles Consulate.