On a TR6, using the rule of 13, which is the same principle as rule of 9, turning the crankshaft the opposite direction of the direction the engine runs, involves much less turning.
I'd like to hear how that works. Seems to me that the engine has to go slightly under 2 full revolutions to get every valve into position, no matter which way you turn it or how you check valve position.
So, for example, on a 4 banger using the "on rock" method, you start by turning the engine either forward or backwards less than 1/2 revolution, until a cylinder comes "on rock" (meaning it is at TDC between exhaust and intake stroke). That means the opposite cylinder is at TDC between compression and exhaust, where the valves are fully closed and can be adjusted. Then you turn the same direction exactly 1/2 revolution, so the next cylinder is on rock, and set valves on the opposite cylinder. Repeat twice more and you're done. Only 1.5 revolutions, plus however far you had to turn initially.
6 banger is the same, except you go 1/3 revolution at each step and do it 6 times.
But the way most people do the "rule of 9" or "rule of 13" goes many more revolutions, because you do the valves in numerical order. For example, the Macy article says to turn until valve #1 is fully open, which may take almost 2 turns by itself. It also takes twice as many movements (one per valve instead of one per cylinder).
There's no reason they have to be done in order of course, but not doing them in order makes it much harder to keep track of where you are. Just ask yourself "If valve #4 is fully open now, which valve is fully open next?" and I think you'll see what I mean. I find remembering the firing order to be much easier (and if you don't remember, just look at the plug wires on the cap).