If you have some basic skills it's not too hard to do yourself. I wouldn't use a saddle valve for the water supply, get a refrigerator valve and stainless hose.
I’d probably call Mitsubishi and ask if it’s possible to calibrate the thermostat. Their tech support number: 1-800-433-4822. They have options in the phone tree for contractor or owner. If the owner rep can’t help, call back and select contractor (be prepared to make up a name of a company)
Yes you can install a humidifier on your air handler. I haven’t seen or used one, but it does exist. Here is an example https://smile.amazon.com/dp/B00R3GEJ6K/ref=cm_sw_r_cp_api_glt_i_226HRNTB8RKTVSS7Z3QS
I don't have an answer to your question but I'm in Saskatchewan and we are looking into whole home humidifiers as well because of how dry it's been. The Aprilaire 500m is the best reviewed and rated humidifier I can find.
https://www.amazon.ca/Aprilaire-Manual-Capacity-Furnace-Humidifier/dp/B00R3GEJ6K
You have to buy it off Amazon as they don't typically sell to the end user. You should be able to install it yourself pretty easily, that was my plan anyways. I can't see everything costing more than $300. Just FYI.