If you have a set of digital readout calipers and if you are using them properly, then you should be able to get the turned diameter to what you want ... for a slimline that measurement should be 0.331" (the bushing diameter).
You can do the turning between centers without any bushings at all and without the mandrels that PSI sells. I would never spend $30 for these:
https://www.pennstateind.com/store/PKMBCM2.html
I do all my turning between centers using a 60 degree live center in the tailstock and a small, parallel sided center in my headstock chuck. . This latter piece I made myself. . And I made one for each of the different pen tubes I use.
At the tailstock end, when you are turning slimlines, you will most likely jam the cutting tool into the live center because there is not much clearance. To avoid that, I don't turn down to size at the tailstock end. I do the headstock end and then turn the blank over so that the tailstock end moves to the headstock and I repeat the process at the headstock end getting both ends of the blank to the size I want.
Now ... at the all-important headstock end ..... As I said, I make a parallel-sided dead center for each different pen tube.
For example, for the slimline, I use a 3/8" rod and machine one end down to 0.325" for about 1". Then I machine a taper on that end and the tapered end fits into the end of the slimline tube. . You now have a mini dead center.
The material for the rod can be plastic (it won't last very long until you have to make a new one), or brass (you will get quite a bit more life but it too will need replacement), or steel (a very long life). You can even use aluminum but it's life will be about the same as brass.
To make one out of steel you can buy some rod at a machine shop (or some tool stores). Get mild steel, not hardened steel). Don't use your lathe tools to machine down the steel, unless you have a metal working lathe. If you pick the rod size appropriately, you won't have to take off much material and you can use a Dremel tool to take the size down (from say 3/8" = 0.375" down to about 0.325" or a shade bigger ... big enough that it won't go inside the slimline tube and small enough that it is smaller than the slimline bushing outside diameter.
Finally, do a shallow taper on the end of the rod so that the tip of the rod fits inside the slimline tube and the "inside corner" of the tube "rides" on the tapered surface.
You can do this shallow taper with a file (or Dremel tool) while the rod is spinning at medium-to-slow speed in the headstock chuck. Use your discretion making the taper.
This is really easy to do, and you can do it faster than the time it takes me to describe the process.
But the overall key to getting your slimline (or other) blank end down to the size you want to match the pen kit hardware components (or a shade bigger) is your measurement process.
Measure when you think you are close. Take the blank in your hands when you measure .... measuring the blank when it is on the lathe does not work for me. Then remount the blank, and turn a little more off the end of the blank keeping to the shape you want the blank to be finally. . Then remove the blank and measure again until you get it right (just a shade over 0.331" to allow for a little bit of sanding).
In a few minutes, you will get the hang of this. . You have to learn to use the calipers to measure VERY close to the VERY END of the blank. . You will notice that the caliper jaws have thin ends right at the open end of the jaws ... use those thin ends as close to the end of the pen blank as you can get and still make a good measurement.
This will take some practice, but it all becomes very natural quickly.
Instead of buying steel rod at a machine shop, you can buy (for slimline use) a thick building spike from Home Depot (Home Depot also sells brass, aluminum, and steel rods if you know where to look).
I hope this helps you. . As I said, I would not buy the TBC mandrels from PSI. I have not tried them but to me they just look like a waste of money. . It is the taper at the headstock end that does it for me by the method I have described. . You can also make use of the taper at the tailstock end when you are working with tubes 3/8" and bigger as long as you proceed very carefully to not jam your cutting tools into the 60 degree live center.
Measure, measure, measure !!
BTW, if you have steady hands, you can quickly grind a taper on the rod on your grinding stone, but I wouldn't do it on the same grinding stone as I sharpen my lathe cutting tools on. For this purpose, a fairly rough grind is OK as long as it is round.
