The Triumph dealer was a might short on shims. The Yamaha dealer 5 miles away had all the shims I needed down to 0.05mm increments. He even had an odd 2.880 where I needed a 2.879. I should able to get much closer to fully lifted valves thanks to the Yamaha shims. If I recall, the Triumph shims are offered in a much more limited choice of 0.25 mm increments. I could be wrong.
As for the famous Triumph cam gear tool, in that there wasn't one readily available to me, and I wanted to finish the entire shim job in around 24 hours, I ground down a couple of inch long Torx bits into dual tapered plugs to hold the split gears together. The Haynes manual does a good job explaining with photos why the tool or plugs are required, and shows how to make a home-made plug.

After rolling the engine over 20 or 30 times with the rear wheel last night, I ended up with all 8 at or near 15 & 25 mm of clearance. Air in. Air out. Air good!
On a side note, I was pleased to see it doesn't take very long for oil to get up through the cams. I had oil coming up through the caps at a half a turn or so. I suppose these oil pumps must hold a prime pretty good.