Bear bottom line you have mentioned a dollar figure several times and for that range, I nor any QUALITY contractor would not touch your job for even the most basic system. You should be budgeting for 2.5 to 3 times that amount minimum Unico w/chiller 20% to 30% more.
I have done several SIP (sandwiched insulated panels) homes ICF and various other very tight homes, I am BPI certified and NCI certified with better than 40 years experience. I have also gone into dozens of similar homes to fix comfort and efficiency problems, all had too much capacity most grossly oversized. I generally need to reduce capacity and airflow as well as increase supply ductwork capacity and return capacity and install Supplemental dehumidification.
I will go over a SIP home I did 5 or 6 years back, 2800 sq.ft. 2-story. We installed a Bryant (Carrier) Evolution 2-ton2-stage unit with a 3-stage heat strips ECM 3.0 blower with Evolution controls w/2-zones all metal duct w/Ultraire 350 supplemental dehumidifier w/digital controller & standard HiEff electric water heater on a timer. The Dehum is scheduled only to operate during occupancy. They maintain 78* 48% RH and their highest electric bill has been less than $90.00.
I would recommend a similar system for you, stay away from gas heat even the HP would more than likely be overkill.