Warbow Flight Arrow &Stuff

I mended the bamboo flight arrow that had split along it's length and reinforced the nock with some horn down the centre and some linen binding. It stood up to the 120# bow but waggled in flight. probably too weak a spine and the fletchings didn't straighten it quick enough.
Flight arrows are a bit of a dark art and my opinions may be complete tosh... so read on but be prepared to disagree! There are plenty of people who know more about it than me.
There are two main main differences between flight bows in terms of the arrow. Centre shot and those that are not, of course there are variations in draw weight and length.
With centre shot you want the arrow stiff as possible, but with a warbow and other non centre shot bows the arrow is going to have to flex round the bow. Because the flight arrow has a much lighter point than a normal arrow IMO it won't need such a stiff spine as normal, as there is less inertia to resist the huge acceleration.
As an example if you draw up an arrow with a point of infinite weight it will have a hard time trying to accelerate and the force from the string will try to bend the arrow, so a very heavy spine is needed to resist the huge bending force. Conversely the arrow with a very light point will have little or no inertia at the point to keep it moving in a straight line and to resist the acceleration and it will try to kick left as the back of the arrow travells towards the centre of the bow while the point is left of centre because of the grip. Because of this a lighter spine will help a true flight by allowing it to flex round the bow..
So what am I blethering on about? My hypothesis is that flight arrows which need to bend round the bow will need to be a lighter spine than expected.

The bamboo arrow mentioned at the start of this tedious post is only spined at 40-45# much to the consternation of my mate JT who shot it from the 120# bow!
Yes it's a bit under spined but not by as much as one might expect, maybe 55-60 would be about right?
So that's what I'm trying to do... stiffen one of those bamboo shafts... but how?
I've started by drilling out down the centre of another 'boo shaft (40-50# spine form the same batch of shafts). I used a red hot length of steel wire to break through initially, but then I brazed a 3.5mm drill bit onto a length of straightened wire coat hanger and carefully fed that through with an electric drill. I'm hoping to fill the shaft with a length of garden cane which I have turned down to size.
How to turn cane down to size? It's easy to turn down a half inch length, but a long bit wobbles all over the place, so I made up a travelling steady to go on the lathe, it sits just behind the cutting tool and supports the shaft, as the cutting tool is wound along the rest follows it.
Video of the travelling steady here:-
https://youtu.be/iJkPsVdw-0c
All this is just a bit of fun, I don't know if it add much to the stiffness, but it's something to try. There are so many variables with a flight arrow. The 'boo is naturally tapered, do I have the fat end at the point or nock end? Do I stiffen the whole shaft, the point end, or just the centre section? What size fletchings etc.
One advantage with a warbow flight arrow is that it should be rugged enough to test over 10 yards in my garage, ideally I want it to have straightened up within 10 yards.

Meanwhile I've finished the rawhide backing on the primitive bow, I'm not sure how well it will stand up, but I have shot it, it looks pretty good, and if it does fail, it shouldn't explode, rather fold up or just loose cast.
DAMN! I've just spotted a crack opening up on the edge at full draw, the rawhide is holding it together, but it's just a "wall hanger" now, still at least I tried. Interestingly the patch has held , but the wood tearing about a quarter inch further up the limb.... maybe I should simply make a bow out of wood shavings and Resintite!