I think you will be OK with a 5/8" blank. . The tube size is 3/8", so that leaves a 1/8" wall thickness after drilling.
But you'll need to drill accurately and I recommend that you do it on your lathe.
Now, with the Gearshift, the PSI-recommended bushings are both the same size.
However, if you measure the hardware size at the nib end and at the top end, you get
0.513" and 0.493" respectively. That's quite a difference.
What I did was turned the blank round at 0.550" and then tapered each end differently to match the hardware size it mates with. . That leaves a slight bulge as you know.
An alternative is to turn the blank round at 0.513" and then taper just one end (down to .493"). . The problem then is that the thinner, tapered end is at the top and that does not look so good.
I think that PSI has messed up their design of this kit.