Wayne, is your car already restored or is it in a condition that needs restoration and where you can remove some parts to inspect this a little further? I think some pictures would be of a big help here as some of what you describe is a car that was originally equipped a/c from the factory. The holes not being stamped into the cowl plenum for the vents, no holes in the dash for the flapper controls at the vents are the only clues present for this to be an a/c car originally. As you are aware, the firewalls are totally different between an a/c and non-a/c car as to the stamped holes for the heater core body and the tube location. So if you have the non-a/c heater box under the hood, then you need to look and see if the firewall has been modified for it to fit. This is not an easy conversion to do as it requires a lot of welding, relocating of a couple holes, and redrilling for the heater box mounting. Most of the time the holes where the heater core tubes come out on a non-a/c V8 (non big block) cannot be duplicated exactly as the factory did it due to the shape of the lower hole. A picture of this area would be good. Also the top of the cowl panel would have to be repaired in the lower corner of the passenger side opening to fill in the cutout area for the plenum valve that is only present on a/c cars, again not an easy proper fix as the underside is not easily repaired w/o some clues showing it being repaired.
What is specifically wrong with the heater controls? Heat operates when it shouldn't, no blower fan speed control, flapper door for vent/defrost does not work...? As for the choices as to how to fix this, well that is up to you and your expertise in working on these systems. Personally if was a factory a/c car then that is the way it needs to go back no matter how much work is required. Since your friend is converting his car to a hot rod then I would get everything from him, including the firewall area and have him repair his to a smooth finish. I have used the Vintage Air systems and honestly they suck. You cannot use your glovebox, the fitment and ease of installation is fair at best. I don't know what you mean as they don't use a pump? Are you saying they don't use a compressor? Well they do, and it does not use factory style brackets to hang it on the engine. The systems do cool well, they tend to have a little more noise from the blower than the factory system, and usually they only use the front center vents for the a/c. I think they now offer a system where it will use the outer vents like the factory system, and you just use two block off plates on the cowl. I just quit using them entirely years ago because of the issues we always had installing them. The last car I restored with a/c was an old drag car and we put the factory stuff right back on there. The owner went with a "Day 2" restoration with period correct speed partsSee attached picture of the engine compartment during the restoration............
If you can take a few pictures of the heater core outlet openings, and of the lower corner of the passenger side cowl plenum opening we might be able to tell what you had originally......................betting it was an a/c car..............RatPack.......................