For future reference for other folks, I did some more digging and found that, indeed, I was so low in my refrigerant after not looking into it for 3 years that following all the instructions to recharge it did not immediately work. Looking at this rennlist thread:
https://rennlist.com/forums/924-931-944-951-968-forum/509239-so-you-want-to-re-charge-your-a-c.html
I see this informative mention of the static pressure of our refrigerant, R134a:
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"In my case they [high- and low-side pressures] are both showing about 80 PSI, and this explains why I'm not cooling much and why the compressor cycles on and off. Here's why: at 83 degrees, liquid R134a has a static pressure [AC not running] of about 88 PSI. If I have less than that for a static pressure, it means that there is NO LIQUID REFRIGERANT in the system. Just enough to be in there as a gas, which is NOT enough to do its job.
...[snip]...
- If the static pressure was 88 PSI: All that tells me is that there is SOME amount of liquid refrigerant in the system. Not how much. A 3000 gallon tanker truck full of R134a will read 88 PSI at 83 degrees, as will a 14 ounce can that you've taken all but 1/2 an ounce or so out of. As long as there is still LIQUID refrigerant, the PSI will have a linear relationship with its temperature."
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I had tried following the refrigerant instructions to fill the low side to 25-35 PSI with the engine & AC running full-blast. As I mentioned, I came to discover that the high & low side pressures were the same, indicating that the compressor wasn't doing its job. I stopped everything, thought about the above post, and figured I was safe in filling the AC system up to ~80 PSI with engine & AC *off*. I didn't want to go much past that, for fear the gauge wasn't calibrated well and I didn't want to go all the way to 88 PSI where the refrigerant would start liquifying -- not until I ran the AC again to follow the instructions properly.
When I started the engine again & ran the AC, lo and behold!
The compressor now had enough refrigerant to "grab" so it could start pumping. Now, the low side gauge read something like 20 PSI -- still low but at least now I could follow the instructions. I'll spare you the physics, but it suffices to say since it was a hot day I leaned towards the high end of the pressure recommendation and filled to 35 PSI. Now I have cold air.
Mind you -- that doesn't mean I have exactly the right amount of refrigerant. You need to evacuate the system & use a scale to really be correct. But it's better than it was, and that's all I was going for this time around.