The support for the ankle is heavily affected by the support given BELOW the ankle, to ligaments and tendons, so although combat boots do give a "splinting" effect a lower cut boot can give more support than some higher cut boots.
Late to this thread an John Fenna is talking a lot of sense.
I've learnt a lot over the years about foot stability and footwear due to my main interest is walking in the hills and fells of the Lakes and further afield. My ankle was always weak and I would turn my ankle about 3 or 4 times on a walk. Often I would end up limping off the hills and spend the week recovering so I can get out the next weekend. I used to walk, since student days, in Scarpa SLs and walked so much I went through a pair in less than 18 months in the end. I used to sprain my ankle a lot, sometimes with that shooting pain that goes up your shin bone as you drop like a sack of 80kg spuds.
My first attempt at a solution was a serious pair of high cuff mountain boots / 4 season. They had a B2 sole unit like the Scarpa Mantas opnly with a higher cuff that also had a very technical cut in thicker, full grain leather (the thickest leather used among the main brands at the time). It had a flex in the right way at the ankle and really was an innovation in boots that even the newer Scarpa Mantas now copy at the ankle. It did not help one bit. In fact I learnt that it did not offer any improved stability and if I did go over the vice like grip on the ankle meant it spread the sprain higher and caused me more pain. I would now take a few weeks to get back into walking the damage was so bad.
Cue a new trend that was happening back then for lighter footwear, even fell shoes!!! I took the plunge with a pair of innov8 roclite 315s. Cracking shoe and one that didn't stop me turning my ankle but I suddenly realised my ankle was free to move as it is designed to preventing serious damage and I often was able to catch the turned ankle before I dropped like a tonne of bricks. 6 months later I had strengthened my ankle and I stopped turning it. I was by now onto my second or even third fell shoe with them lasting about 2.5 to 9 months. Nope, I was on my second which was the discontinued Montrail Highlander (lasted a personal record of 9 months).
SO my advice based on hard won experience is that if it is walking in the hills you need to strengthen your ankle. You need to allow it to work as it was designed which means no rigid splint. That only drives the damage further up the leg, well rather it damages your ankle but spreads the damage a bit more. At the very least I found that the top of my ankle was fixed with the cuff and the laces gripped the lower / foot. Result was the actual joint components (the tendons ./ ligaments not sure which) got kind of stetched and damaged.
If I was you (and I was a good few years ago) get a good pair of mids. If you read the expert advice on some gear reviewer magazine articles you often read comments like the stability comes from the footbed and the way the heel cup grip your foot not from the cuff. I think in the better military boots they are realising this too.
Please note that I am not recommending trail shoes for everyone. I only did it for myself and it worked. What I am advocating is to allow your ankle and foot to work how it is meant to by not putting it in a rigid outer covering (high cuff boot). Perhaps take shorter walks using mids or fell shoes. /build up. Mind you if you want to try the fell shoe approach bear in mind it takes at least 6 months to notice a positive affect IME. It is no good trying it for one walk and saying it doesn't work. I would say I was doing over 1000 miles a year with all the challenge walks, most weekends both saturday and sunday walking 15 miles plus a day and often evening walks. I did 50 milers once or twice and every year a 40 miler for charity with associated training walks. Well it wasn't a race but you always wanted to beat some people / certain teams you keep meeting each year so you did train for it.
I hope you sort your ankle out as it is not fun getting injured doing what you like and not being able to do it for some time. Been there, bought the ankle supports, deep heat, ice packs, bandages, pain killers and doctors visits. in fact the whole gammut short of surgery and buying the t-shirt!