Hi,
For a TR6 engine, I believe the quoted oil pressure is 40 PSI @ 2000 RPM with an SAE30 oil @ 80c. At 80c I believe 20W50 is the same viscosity.
I think if you use a thicker oil at 80c you need to aim for higher than 40 PSI.
The Chris Witor Triumph Specialist pump clearances are very good. Further work can be done with a Dremel if you are bored. Mine is sitting in a box with 3 kak-looking bolts.
Cheers,
Iain.