Stiffener does give you a little more time, but even stiff hats will taper. But, no other felt will keep your head as dry, for as long, than beaver felt.
I have gotten back a few of my hats that looked tapered, when it was nothing more than the hat settling into a tapered look, when the top cent sunk down too low. Also, a 5 3/4 crown hat will do this quicker than a 5 1/2 crowned hat. Also if the hat is soft, sitting it on its brim as a habit will make the hat look tapered, as we have seen here in the past when brand new Optimos were pictured, sitting on their brims, and they looked tapered, when they were actually not. But, this is not the case with your AB Tone, as you said it was taperd while on your head.
A copious amount of steam is an enemy of any new felt. You can use a small amount to style the hat, but if you use too much, it relaxes the shape, because steam relaxes the felt itselt. Once the felt is relaxed, and not on a block, when it dries, it can shrink in order to become tight again.
I have owned every Indy hat out there, and it has been my experience that the AB sure lasted longer before tapering, than the other hats I have owned.
I am afraid the nature of new felt at least, is to shrink, when exposed to heat and water. And untill the felt dies, which can take 5 to 8 years, reblocks will be needed if you want to keep the pristine straight sided hat. On a hat that is tapered like the TOD hat, since the hat is already tapered, these will hold that shape for a whole lot longer, in fact, they may never need a reblock. The hat starts out as a cone. If you make a square shape out of the hat, it has been stretched out in order to do this, on the top of the cone. The only thing that seems to alleviate this is the age of the felt.
The ageing deal that Marc came up with, may add some time to how long it takes for a reblock to be needed, but it will not eliminate shrinkage in the same way that an truely aged hat will do.
Back in the old days, there were scores of hat shops and scores of dry cleaners. They all offered reblock services. This shows you that nothing has changed in hats from then to now.
What I need to do is to run a comparison of a beaver hat versus a rabbit hat and subject them to the same thing. I think you will see the beaver will not taper nearly as fast as a rabbit. I have experienced this personally in my own 7000 dollar collection of hats.
Although your hat appears to be tapered, it looks nothing like some rabbit hats I have seen here over the years that had tapered. Many of those rabbit hats were pointy on the top due to the extreme taper.
If that were my hat Tone, I would pop out the crown and use a hand held steamer, to steam the hat, the upper half. Then I would put my fists inside and punch the felt out on the top, and upper sides, where the taper is. Push your fists apart like you were doing isometric exercises. Steam again and repeat. Many time the hats that I get back suddenly are not tapered anymore. Then let it dry in the open crown state. Once it is dry, re bash it again. It is worth the effort, in most cases.
For me, if I were a serious hat wearer(which I am) I would invest in the next smaller size block and periodically pull it over the block to maintian that straight sided look. Afterall, you see so many vintage blocks on ebay that came from the estate of some guy who passed away. They used them back then to keep the hats looking new.
But if we are looking for a new felt hat that will not taper with time and wear, there ain't no such animal that I know of. Felt is made because it has the ability to shrink to a particular size. When they size hats in the factories, they just shrink it down in boiling water until it meets the specs of a particular size. If felt would not shrink, you could not even make fur felt as the shrinkage is what creates the felt. There is a point that felt will stop shrinking, once it shrinks to a certain point. But, since the body started out as a cone, you would have a smaller hat, that looked like a cone.
I have vintage hats that will not shrink, or shrink so very little that you cannot notice it. But the felt has to die in order for this to happen. And that takes years.
I just caught the above quote from Tone. That is exactly what I see in some of the reblocks. The top crease deforms, by getting deeper, and that in turn, pulls the sides of the hat inwards. Once the felt "sets" to this the problems arise with the taper. I know this sounds nuts, but what I used to do to my own hats, and not necessarily ABs is the old ruler trick. I recrease the top of the hat, after a bit of steam from a hand held steamer, and while the hat is still warm on the top, I beat the top of the hat with a wood ruler, which flattens out the humps, and it also pushes the top side of the hat out. Sometimes I do this many times, until the hat looks right again. I have had excellence results from using this. Give those a try and see if it helps. Fedoraand the top dent has to be pulled wide (and inaccurate) to get the sides to stay halfway straight at this point.
Now I REALLY can't wait to get mine. 
Great looking hat.
