Unbiased Opinion

[Irascible]

I will call the companies that I have received estimates from and see if I can get a copy of their load calcs.

As has been implied, it's not likely that a real heat load calculation has been performed. They may say they've done a calc. But a real room by room heat load calc can take a few hours, sometimes more. Throw in the rest of the design (duct sizing, diffuser selection and so fort) and it's taken me an entire day to design a complete HVAC system. I'm sure some guys are faster.

Getting that kind of analysis as part of a so called free estimate is pretty tough. You might be able to find a contractor desperate enough. But just as likely you may find that only a minority even can do a real heat load calc. Most use rules of thumb and goofball short forms. Of those that do the real deal, I'll be surprised if they'll do it for free. At best they might do a quick whole house heat load calc.

If they hand over a calc see if you can find out how it was produced. A simple one page form with blanks filled in, or anything like that, isn't a Manual J heat load calc.

[Zeiss Nut]

Get one unit sized properly for upstairs first.

Then in 5-10 years get another one for basement when it is finished.
In my experience you could never get the temperature and comfort to equalized between first floor and basement .

The basement going to be colder in the summer and in the winter.