help installing a regulator

There are questions about both the compressor operation and setup.

1. The HF compressor comes with a bleed regulator. You should use it to adjust the output pressure instead of adding an external regulator.
2. It is true that this type of regulator does not work well with very low pressure, but should be fine for down to 15 psi or slightly lower which should cover most modeling pressure needs.
3. Your pressure reading will drop some, up to 6-7 psi, with the HF setup, but should not be from 45 to 20 psi. It is a clear indication that the bleed value is not setup properly.
4. Yes, you can replace the compressor regulator with a better one. But you need a true diaphram type regulator for better operation. You need to talk to the vendor to assure that they are selling you this type. (Most vendor sells both because the buyer just want it cheap.) You can also identify them by looking down the pressure port which should be a small hole of 1/8" or so. Paasche and TCP Global both had one at about $30. Iwata and Badger ones are as expensive as the whole compressor.
5. The cheapo, made-in-China, air regulator sold for airbrush compressor are usually just a adjustable orifice. Its reading fluctuates and the setting is touchy. They sell for $12-20, but are pretty useless. The pressure port is large hole.

For your setup, I will recommend try to learn to use the breed regulator and compensate with your skill. When you can afford a better compressor, it will come with a better regulator.

I would suspect the regulator more than the compressor. If it does not have enough flow capability it can produce the slow drop.  Try adjusting the needle to get less flow and the regulator may regulate a bit better.  Still, I have used regulators that did that and you can compensate a bit in your airbrushing technique.

Excellent!  I used a combination of the bleed and the reguklator valve and it holds a steady pressure after the initial bleed down. The compressor does run constant, but it's easy to shut it off.

Muchas gracias, amigo.

Don't be so hard on yourself. I used a HF compressor and airbrush for a number of years and, for me, they worked fine. From your description, I think you're referring to the compressor/AB kit. If so, that compressor has a bleed regulator (unscrew the valve at the bottom of the moisture trap to regulate pressure). Turn compressor on, depress AB valve and adjust pressure by opening/closing the valve. If you do so, the compressor will run continuously while it's on but at a constant pressure after the initial drop. I'm not sure what you mean by 'glorified valve' but if a simple constriction in the line what you describe will happen. A number of compressors have the 'bleed valve' regulator (Iwata Smart Jet for example) and if you don't mind continuous running while you use your AB they work but so-so in my opinion. That compressor does have a pressure switch built in so you could close the 'bleed reguator' and add a proper regulator down line someplace if you really want fairly constant pressure. I modified one to a 'non-bleed' regulator.