I am really surprised that the Triumph shop manual (and even the Triumph competition tuning guide) makes no mention at all of even checking the head for straightness, much less an allowable amount of warpage. I wonder how many warped heads have been reinstalled over the years??
I am turning to my engine building books for the Ford 1600 engine (also a pushrod 4, though I think physically a little longer than the TR engine). The definitive FF1600 racing engine book simply assumes that the cylinder head will be resurfaced any time it is freshened (not necessarily every time it is removed). A much older race engine building manual says much the same. The most authoritative book on 1600cc Ford street engines says
"I am not going to lay down how much clearance is too much. It depends on how far you are going in your power tuning. For top power on a racing or rally engine, any clearance is too much, and having the head and block refaced is almost mandatory.
...
"The decision becomes more difficult if you are just overhauling the engine... I have overhauled engines with up to .003 or .004 in warping between the head and block without having any long-term problems. As a general counsel, if you are having the block rebored, have the block and head checked and, if necessary, refaced as well."
Maybe the reason that nobody specifies a number is that a warpage of 0.002" from one extreme end of the head to the other extreme end is a little different than 0.002" of warpage from one side of the head to the other?