Steady there Steve (yewArcher)
I understood what you were saying. Personally I don't whip my own arrows. Looks nice but can't be bothered with it. If aunthenticity is needed then I'd use silk thread to cut drag, covered with perhaps some pva with something snot green mixed in. I only whip the shaftment just below the knock as a belkt belt and braces approach, in case the shaft splits. Which incidently has only happened on pine arrows but not on Hazel or yellow poplar (tulipwood).
icindentally, in the "great warbow" by Strickland/Hardy, there's a picture and description of the Westminster arrow. It says the knock reinforcement was inserted across the grain. A personal friend who saw many years ago (memory has faded) says it's difficult to tell which way the knock was cut as it's made from poplar and as it was found on the roof of the abbey, it's gone black.
I intend to make an arrow with the reinforcemnt as described in the book to test if it works any better.