OK: the first one is done, and I'm very pleased with the outcome.
A "standard" interference fit is something like 1 thou per inch of diameter, so the if the pin is to be pushed in and stay there the 1/8" hole has to be just a fraction of a thou smaller than the pin. Fiddly.
My procedure was very low tech, and is the sort of thing that can be done in most sheds with very little equipment. I made a very slightly tapered cast iron cone on the lathe, about 0.120 at the pointy end and 0.125 at the thick end, about an inch long. The plan was to use this with valve grinding paste as a lap to increase the size of the hole just a few thou. I ended up doing the lapping by hand. (Doug don't read the next bit!) I mounted the lap in the jaws of my Vice Grips, and held the Vice Grips in my bench vice so that the lap was vertical and well away from the vice so the foot of the tappet would clear the jaws of the vice. I then just applied grinding paste and worked the tappet back and forth on the lap as if grinding a valve. The centre of the tappet is hollow where the hole is drilled, so it was more a task of opening out two rather shallow holes rather than one deep one. Just flip the tappet over regularly to work on the other side.
The progress of the hole size was measured by how the far down the cone the tappet moved. I also stopped regularly to wash the grit off and make independent measurements, using my various drill shanks and the tapered shaft of my scribe, some engineers blue and a micrometer. As I got close I offered up the roller (from an friend who has Indian motorcycles - "help yourself"). I had one gentle try at pressing the pin in (using my vice), but it was too tight. Open the holes out just a bit more and it pressed in nicely.
On assembling the tappet in its block, it feels excellent. Glides in and out, no free play when oil is present, a tiny bit of rotation (a couple of degrees probably) as the pin rotates in the slot but no roughness if I rotate hard in each direction and slide the tappet in and out.
Time? A few days thinking and measuring, a few wasted hours, then about 90 minutes of work. Cost? Nothing. Satisfaction: unmeasurable.
On to the next three. Thanks for all the helpful suggestions.
Leon