Hi Thomas,
I'm with you on this – I had a ankle fusion about 16 years ago on an injured right ankle. As a result my ankle is fused at a slight pronated angle, and my right leg is a bit shorter than my left. I've spend a good part of the past 10 years (and the project is still ongoing) learning about how to adjust my shoes to compensate.
I actually AM a physicist (LOL). It has helped a bit, but I can tell you I have not discovered any really good information on "boot theory". I have several hundred dollars worth of medical books on biomechanics of the lower extremities, but I have never found a book on what you are asking about. I'd buy it in a second if I ever found one.
Even more depressing is I have had some world class surgeons and gone to many podiatrists and none of them has been the least help. The way I describe it is that they are only interested in "functionality" at the level of walking from the couch to the refrigerator, not for hiking 10 miles through the mountains. The usefulness, in my experience, for getting some of these problems solved in the form of adjustments of your footwear, from least to most helpful is (1) surgeons (totally useless), (2) podiatrists (almost totally useless), (3)othodists (19/20 pretty useless, but if you can find one that will work with you in detail they can be very helpful). Most of the above can be useful in telling you exactly what the problem is, but if you can't cut it off or screw it together they don't help much for the long term mechanical issues – at least for the bigger issues such as yours and mine.
The most important detail of course is exactly what is wrong with your ankle. You don't say too specifically, but I take it that the lateral stability of you ankle is shot, that you tend to hyper pronate or supinate (assume the former at it is the most usual) at this point with minimal "encouragement" when you walk, and you have already more or less done everything you can to reinforce your internal ankle strength. Therefore you need some external support to minimize this issue.
Congrats on discovering the truth about high boots for yourself – high boots (except ones that are so huge as to defeat the purpose of "normal" walking) will not protect your ankles. On the contrary, to the extent that the *decrease* your feel of the ground that can make things worse. So the real issue is no shoes can keep an ankle from turning and big boots tend to actually increase the probability of that happening. So the focus should be on prevention, NOT mitigation.
Your second observation I think is also right on. You want to be close to the ground – the leaver arm when you do turn you angle is just going to increase. You may need a stiffer sole on that foot, but you can buy carbon fiber shoe plates (inserts) that weigh nothing that will add all the stiffness you need.
Your third observation of a stiff shank is also right on, withyou issue you may have other concerns. You may in fact want a stiffer sole, but may want to give up on that as an intrinsic par of the shoe to find a good solution for you. There are some other solutions for this.
So… how to solve your problem. I would say find a decent orthodist that can make you both custom insoles (super important in this case) and possibly other orthotics and make custom modification of your shoes if necessary. Make sure he or she is willing to work with you to tweak things, and is willing to let you tell him what you need and what works for you. There are places online where you can have some of these things modified if you can't find anyone close by.
That said, here is one way you could analyze your things if your main problem is that you have bad lateral ankle stability you want to support this. As you already noted even a large leather boot is not going to stop your ankle from turning. So short of putting on some kind of heavy brace are talking about measures to *prevent* things from getting that far. The naive and uninformed point of view, which you have already partially shot down would be simply to support the ankle in the lateral direction. This doesn't work by itself. You need to prevent, to as large a degree as possible, the over pronation or supination in the first place.
To start you probably want to get some custom insoles made – the ones where you get casts of your feet made. These will tend to stabilize your ankle when your heel strikes, and that is the absolute first thing you need to get that pinned down. If your insoles do not fit your heel (at the very least) like a glove then you need to fix that. Second buy shoes with a wider heel. Get a cheap micrometer and bring it with you to the store to measure this.
Thirdly, the way the foot works is that it rotates (pronates) as you go from heal strike through to push off. So every time your ankle flexes while walking it will naturally want to pronate. Depending on the terrain, and other physical things happening on a particular step this natural pronation can easily turn in to hyper-pronation (turned ankle). So provided you have already done the easy steps above of custom insole and wide heel, the next step is the less intuitive more drastic one of stabilizing your ankle motion in the perpendicular direction – the less you ankle has to bend the less it will also have to pronate. Short of using a custom brace, which depending on how bad it is you may want to do after all the other things are tried, minimizing the flexion of that ankle means either a stiffer sole or a rocker bottom, or better a combination of both. You can stiffen a soul using very thin, very light carbon fiber plates (about $50-60). These are like insole that go under you regular insoles. You can get the soles on your shoes modified to have more rocker style bottoms, and these can lower the about of pronation during a normal stride, and possibly lower the tendency to hyper-pronate. These modifications can allow you to walk with less pronation in your stride,
All of the above said, remember the following. Tweak things lightly, one step at a time. Remember to follow the advice of using the modified footwear only for a few hours at a time until you feet get used to them. Lastly keep in mind that there is a price to pay – what you are doing is knowingly altering the way you foot works, and will be playing off some other forms of flexibility and stability to fix you specific problem. The important thing is to test at each stage, and then tweak some more. You want to find a balance point between trade offs that works for you. Unfortunately you are going to have to be the driving engine to get this done – long before you get to the end you are probably going to be *telling* the orthodists what you want them to do, rather than asking them. Don't do anything you doctors thing is just wrong, but when they start to shrug you will know it is time to be proactive.
BTW, trekking poles another *essential* addition to the mix here. If you are't using them with what you describe as your problem, then that is thing number one. A very good idea. At this point I just assume people who wear trail runner use them. LOL
Hope this helps a little and good luck.
ps. you are going to get a bunch of advice on here from the standard groups. People who say the foot is perfect as it is and you should wear less (total bull for people like us who have some permanent damage and DON'T have a normal foot). People who say you can train or strengthen you way out of it (good advice but also bull for people who have permanent damage) and so on.