Symmetry or Not?

Warning! This could get tedious!
Most bows aren't symetrical. A longbow is fairly symetrical but the centre of the grip is usually a little below the true centre of the bow and the arrow pass about an inch above the true centre. This compromise gives a smoothly working bow. This assymmetry also gives rise to the practice of making the lower limb slightly stiffer than the upper.
On the tiller, any assymetry can look confusing* and one trick to overcome this is to reverse the bow and look at it round the other way. E.G. I always have the top limb to the right, so I flipped the bow I'm doing now to see it it with the top limb to the left.
Whaaa? It was maddly out, the bottom limb tip was much higher than the upper.
(The normal way had bottom tip about an inch higher at full draw, whereas it was about 4" higher round the other way!)
I shifted it on the tiller a bit to make it look right and wondered how it could be so different round the other way.
The only answer could be the tiller isn't set up true, then I remembered...
Ages ago I had rather hurriedly made a new support block (that the bow rests on) which holds the bow about and inch or two away from the wall when I was tillering a very crooked stave. I make the block curved at it upper surface so the bow can rock back and forth as if lightly supported in your hand. Maybe I'd made it lopsided?!
A quick check with a plumb line and spirit level revealed that I was off centre by about an 1/8" to the left but the curve was skewed too making the left side higher, all in all it was probably nearly 1/2 an inch out to the left. (But between having the bow one way and t'other the difference would become 1")
In the grand scheme of things 1/2" isn't a big difference, but conversely, why have it wrong when a minute with a rasp and making a new pencil mark can leave it spot on?
Sorry if all that was a bit laboured, but I see pictures posted on Primitive Archer by people wanting advice on the tiller of their bow as it progresess. The tillers are sometimes all on the skew and the bow clamped in the centre so it's not free to move.
Any measurement is only as good as the reference point.
I realise we can't all have a standards laboratory as a workshop, and indeed mine certainly isn't. I've even used a tiller tied to a tree, but I tried to get it vertical. It does illustrate that my policly of always have the top limb to the right was at least putting some order into the uncertainty.

*When a (long)bow is on the tiller resting as it will in the hand and drawn from where it will actually be pulled it sits rather tilted early in the draw. As it is drawn further, this tilt slowly corrects. It's tempting to clamp a bow on the tiller dead square and pull the string from the centre. I do this on occasion, but bear in mind it isn't representative of a real draw.
I try to minimise the effect in my video clips and pictures to some extent by supporting the bow, just below the arrow plate, which would be a reasonable simulation of shooiting with the weight of the bow is taken on the ball of the thumb, rather than the palm or heel of the hand.
After all the tillering in the world, the real full draw photo can still be revealing.