...
3. With the unexposed negative (representing Zone 0) in your enlarger, make a test strip on your preferred paper at grade 2. Dry this strip and look for the first time revealing black. This will be the segment whereby you can't make out any other segments as your time got longer. At this point, you have your SPD (Standard Printing Density.)
4. Without changing anything, put a Zone VIII negative in your enlarger and expose a piece of paper using your SPD. Cover half with a card. Dry and evaluate. What you're looking for here is a very slight density between the exposed and unexposed sides.
...
In that case, print the zone VIII negative on your paper with a coin on the paper, you would want to see just the outline of the coin. Your print exposure time is the minimum time for max black on the rebate.
If you can't see the outline of the coin, decrease development of the next negative. If the coin outline is very obvious, increase development of the next negative.
My first enlarger was an old Omega B22 condenser from a flea market. I followed the directions above to learn my exposure/development time which ended up somewhere around 5.5 mins in D76 1+1, and even that was quite contrasty to print at grade 2 with that enlarger, but I didn't know any better. Fast forward 7 years and I am now a nerd with a densitometer and I can tell you these negatives are severely underdeveloped for printing with a diffusion enlarger, most require grade 4, and if I'm using a softer paper like Foma 131 I will have to print at grade 5 and even then it's a low contrast print.
I'd seriously consider if this is the enlarger you plan on using for the long run before you commit to tailoring your negatives to such a low contrast. And if so, I'd think about using grade 1 as your target instead just in case you ever end up in a diffusion/soft paper situation.
...
I can see several possible ways your calibration is going off the rails.
First, unless you have a really reliable way to measure Zone I density, you're stuck with using the visual method referred to above, which is based on your finding the minimum exposure time for maximum black on an unexposed but developed area of the film and just a hint of difference for Zone I. This is much harder to do correctly than it might at first seem. The lighting for print viewing is critical; too much light and you'll see separation that you wouldn't in "normal" lighting, causing you to give more exposure to get max black. Too little light and you won't see the separation you need to, causing you to give too little print exposure. You can see what that will do to the highlights; too dark in the first case, too light in the second.
Plus, if you're using a paper with a shoulder slope that is not very steep, there will be lots of steps of separation to see, just not much density difference between them. This means that max black can be quite elusive.
So, try your printing the other way around once. Print your Zone VIII so that it is correct and see what the blacks look like. Even print your Zone I and clear negatives at your Zone VIII time and compare those.
Also, try to use lighting that you consider ideal for print viewing in a gallery; not too bright (don't walk outside and evaluate the blacks in the sunlight!) or too dim (regular living-room-level lighting). The whole point is to make prints with acceptable blacks and fine highlight detail and separation, Don't obsess about max black (you can always burn), but rather how the middle Zones are rendered and how the separation and local contrast seem to you. Really important is the rendering of Zone III and Zone VIII.* (see below!)
Second, realize that a condenser light source prints a lot more contrasty than a diffusion light source would. If you ever plan on getting a diffusion enlarger, xtol121's advice about using a lower contrast grade than grade 2 as your target might make life easier for you in the future.
And, since we have VC papers with such a wide range of contrast control nowadays, you don't need to obsess about hitting your target grade exactly every time. You can always tweak contrast a Zone or two either way as long as your negative density range is within the paper's limits.
And, a third thing: Do make sure you are developing your paper long enough. If you're using fiber-base paper, 2..5 to 3 minutes is the minimum you need to develop optimum separation in the low-density areas of the print (highlights). A minute or so longer won't hurt; it's basically like adding a bit more exposure time. If you're in doubt, develop a print for five minutes. If there's a significant difference in highlight separation for what you can get with shorter development times, you need to develop longer.
And finally, be aware that using LEDs for your exposure tests will likely result in different results than using daylight. Go outside and find a real-life subject with the Zone distribution you want and photograph that, keeping good notes. Use an E.I. of 2/3 stop slower than ISO speed. Pay special attention to placing Zone III, but have some darker areas there that meter Zone II and Zone I. Also make sure you have a textured white that you want in Zone VIII, but also some middle Zone V - VII values. Keep notes. Make several negatives. Develop one at your trial development time and print it so Zone VIII is where you like it. Then compare mid tones and shadows to what you metered. If you need more separation between Zone VIII and the shadow values, develop the next negative longer and try again.
Yes, I know this seems backwards from most of the recommendations to find a max black time and then see what the highlights look like, but, if you rate your film 2/3 stop lower than box speed and your meter is halfway accurate, you will not be underexposing your film. What you need then is a development time that gives you the desired contrast between Zone III and VIII. This eliminates the need for the max black visual assessment, which is the point at which most print exposure mistakes are made. Give it a try.
* Warning: There are at least two versions of the Zone System commonly described, one in which Zone I is essentially max black, Zone VII is a barely-textured white and Zone IX is essentially paper-base white and another in which Zone I is close to max black, but Zone IX is a barely textured white and Zone X is paper-base white. Make sure how you want your Zone VIII to look. For me, Zone VIII is the lightest Zone with some texture, e.g., textured snow, bright sand, and Zone IX is a textureless very, very light grey.
Hope this helps.
Doremus