Sorry to hear about this; I know unaccounted expenses can be a big headache and stressor. Hindsight 20/20 but wanted to offer my thoughts.
If you have reservations about unresolved inspection items before the objection deadline, this should be communicated with your agent. There are a couple of possible solutions, which most sellers are understanding of and will work with to keep the deal together. Your agent should have it as a priority that you are at peace of mind prior to moving past inspection. Here's a couple solutions:
1.) Amend the contract to extend the inspection related deadlines. Delays happen, by no means is it game-over if you are unable to get further expert opinion on a particular item.
2.) Have a clause in your inspection objection that reads along the lines of, "The seller agrees to extend the buyer`s inspection termination / objection period for the HVAC as the buyer was unable to schedule further inspection prior to Inspection Objection deadline"
3.) Write a contract with longer time alotted for inspections as you suggested. Some sellers may object to this in a counter as it's pretty standard to have inspection resolved within the first business week. Not to worry as you have the above two options once under contract and are more in the "driver's seat".
Once pending and under contract, last thing a seller wants is for the deal to fall apart and they have to go back on market after being off for weeks. An amendment to inspection related item, especially a very reasonable one in this case, shouldn't be an issue for most sellers to work with.