To answer your question about tracking, knurls can mis track and produce a double pattern that is half the pitch of the wheel. However, they are also somewhat self compensating in that some slippage will occur as the wheels go around the work.
Each knurl has a particular pitch which should be specified when you buy it. The general held thought is that your circumference should be a multiple of that pitch (25X, 26X, etc.): at least approximately. If your circumference is half way between such a multiple (25.5X, 26.5X, etc.) then there is a good chance that mistracking and doubling up will occur.
So, as I see it, the trick is to adjust the diameter (circumference actually) so that you are closer to a whole multiple than to a half. Or pick a knurl size that works with your diameter. This may be possible if you look around as they are available in several pitches in either inch or mm units.
On the diameter of the knurls, I don't think that will make any difference in the tracking. But for small diameter work, smaller wheels are better perhaps as the work has to fit between them.
I would stay away from things like pipe cutters. One thing necessary in the tool is rigidity and no play. Pipe/tubing cutters are made with very loose tolerances that will cause trouble when knurling. I made a tool with a pair of slip joint pliers but it is difficult to use. You are actually better off with the cheap imported tools. If you are making a tool, do not allow too much slop in the pivots.
On a drill press, three wheels are an absolute necessity. You would never be able to keep it on the work otherwise. For a diamond pattern, you need one left and one right hand diagonal wheel. Someone may make a single diamond pattern wheel, but I would bet it is expensive. You may be able to use a plain roller for the third, but I would not even try. Rubber would be too soft for the forces involved. Heavy pressure is needed for knurling. Aluminum may work initially but will deform and distort under the pressures and eventually turn into a knurl shape itself. But it will continue distorting and will likely need to be replaced in short order. Harder metals will tend to flatten the pattern you are trying to make so they wil be counterproductive. Knurl wheels are relatively cheap so I would just buy two lefts and a right or vice-versa.
Another thing to keep in mind is control of the tool. Large forces are needed to knurl metal. With stainless, this is to be emphasized. It will be hard to keep the tool on the section of the work where you want it. This may be OK as you say you are not working to a particular shoulder or end point, but will be cutting to length after knurling. But it may be difficult to move the tool along the stock. You will need to either have a good, long handle for a good hand grip or the tool will need to be locked down (perhaps with some room to wiggle) to the drill press table and use the quill down feed. I think I would try the lock down idea myself, but I have no experience here.
You might want to consider an easier metal to work with like aluminum or brass.
Make it fit.
You can't win and there is a penalty for trying!