A few points here.
First of all, is it particularly crucial that it be steel? If you can use cast iron instead, the raw material costs around half as much:
($129.29 for an 8" x 3 1/4 disc)
Whether cast iron works for you depends on what you need from these rings though. Steel is tougher and stronger, were cast iron is fairly brittle. On the other hand, cast iron tends to be more stable, so it may fit better with your concern for maintaining its outer diameter precisely.
If you were doing to make these on a lathe, I see only two reasonable choices:
- allow something like 3/8-1/2" clearance between the ID of one ring and the OD of the next smaller, to fit a cutter that you can extend 1.5" out of the tool holder and still have at least semi-decent rigidity.
- make one set of rings from 2 blanks, so one blank produces 1, 3 and 5 inch rings, and the other 2, 4, and 6 inch rings. This gives you 1" for each cut (plus as much more as you want clearance between them).
For what it's worth, the tool you want for this isn't a parting tool, it's a trepanning tool.
The other possibility would be to use a milling machine. You can use an extra-long end mill with a fairly small diameter (e.g. 1/4th inch) to make the cuts.
For this, you'd use either a CNC machine, or a rotary table. Put your blank on the table, cut (just over) 1.5" in from one side, flip it over, and repeat. Since you apparently care about the accuracy of the OD, start by cutting each a little oversize. Then do a quick pass on the lathe to clean up any mismatch between the two cuts and get the OD more accurate. Depending on the accuracy and finish you require, possibly a final pass on a center grinder to get a finer finish and higher accuracy.
Just for grins, I did a quick facing pass on the lathe with a 3/8ths inch cutter sticking a little more than 1 1/2 inches out of the tool holder. Definitely needed to stick to light cuts, and it still got some chatter, but nothing so terrible it seemed like you'd be breaking bits gratuitously, or anything like that.
That's probably not the best possible test though. I used a carbide cutter, but they really cut their best with heavy cuts (deep cut, fast feed, or both). With it sticking out that far, you're kind of stuck with fairly light cuts. A HSS or Cobalt cutter would probably work a bit better under the circumstances.