It is well established that SIPs homes are well insulated and tightly constructed. Taken together, those attributes make design of a heating, ventilating, and air conditioning system for a SIP home a difficult task because there are much smaller heating and cooling loads than in homes constructed with more "conventional" approaches. The low air leakage requires a mechanical fresh air ventilation system. It appears your HVAC designer/contractor won a trifecta of failures--one in each of the above categories. Not surprising. Most aren't design professionals.
You'll need someone to take a comprehensive look at the HVAC requirements in your home. It's likely you'll need to do more than one thing to remedy the issues you have.
The current recommendation from ASHRAE is a minimum of 0.35 air changes per hour in a home. For "calibration purposes," a blower door test of a SIP home we have nearing completion suggests a natural air infiltration of approximately 0.1 air changes per hour. Albeit a single case study, your results will probably be similar and you'll likely need to install a HRV (which is more appropriate than an ERV in your climate zone.)
You'll need a ventilation strategy for point-sources of moisture such as cooktops and showers and make up air--the same as you would in any other home.
You will likely need to install a dehumidifier to provide dehumidification during those periods when relative humidity is high, but there is little or no demand for air conditioning. Maintaining indoor relative humidity at or below 50% is generally recommended.
Before committing to any of the recommendations of the various HVAC contractors or my recommendations, I think you'll benefit greatly by reading Joe Lstiburek's book "Builder's Guilder to Structural Insulated Panels for All Climates" at your earliest convenience. There's a section on HVAC. There's a good chance you'll know more about HVAC after reading the book than the HVAC contractors selling solutions.
Q