Thanks a bunch Desert XL- I think the link you provided will be of great benefit!
Just to reiterate, the 3rd gen galaxie factory air con has no blend door. Which weirdly the 3rd gen non factory air con heater does. As a result the only way the heater (heat) output is controlled is by regulating the flow of coolant through the heater core. So just because it may seem like there is coolant flowing, doesn't mean it's enough.
Here's two simple diagnostic tips that do not involve taking anything apart and only takes a few moments. First, the only vacuum driven air selector door in the dash that could cause little heat (bypassing heater core) is the recirc door (aka Max A/C).
Here's a simple test. Start the car and put it in heat and warm and blower on high. If that door is open or partially open the blower motor/wheel will seem really loud as if you look under the passenger side dash if it's open or partially open you should be able to see directly into the squirrel cage blower wheel. In heat mode this should be closed all the way. Another quick test, with engine running, slide the temp selector from heat to max a/c, the blower should get louder. Then back to heat, should be quieter. Repeat a few times to make sure noise levels are repeatable (door not sticking) if it's too hard to look at the door from the under passenger dash. This door is designed to be either fully closed or fully open. Anything in between is a failure (check vacuum lines, door hinge, seal and vacuum source).
The last simple test is checking if there is enough coolant flow through the heater core. Start the car, let it reach full operating temperature, then put it in heat, all the way hot and blower on high speed. Let it run like this for a minute or two. Next open the bonnet and feel the heater hoses leading to the hidden heater core. They should both be hot, if one of them is warm and the other hot, there is not enough coolant flow.
If this is the case, put a vacuum gauge on the hose at the heater control valve at this point, it should be at least 15 inches of vacuum at idle. If not, go through the vacuum lines. If there is at least 15 inches of vacuum then it's either the heater control valve, heater core, plugged hoses or fittings in the engine (have seen this believe it or not).
With these two quick diagnostics it will give you a good place to start without starting at one end of the system and working your way through the entire HVAC. Although with a 50+ year old car I would highly recommend it if you wish it to be reliable.
p.s. Thank you puttster for adding the notes to my picture, glad you like the photo.