Great question. Not an easy answer and maybe not something you really want to pursue.

Option 1:

If this Soldier has a permanent injury to his leg/foot then the hospital has a section dedicated to making them a special boot to wear. We personally know individuals who have had this done. No waiver or even chain of command involvement is needed. Just needs to talk with his PCM.

Option 2:

Apply for a Wavier/Exception to Policy

You would have to apply for a Waiver or Exception to Policy. The 1^st step in that process as a matter of professional courtesy would be to run this request through your Chain of Command so that can assist your and so they are not caught off guard should a request for additional information come back down through official channels.

Keep the Chain of Command Informed

While you have the right to make the request it is always a good idea to ensure your chain of command is fully informed and they are not surprised. By working with your chain of command they may have another process that is more effective than the one that is suggested here. The Chain of Command could potentially provide letters of support or recommendation concerning your request.

Possible Process

The steps you might consider in this process might be:

Obtain a recommendation from your doctor. This could be a double edge sword. If you cannot wear an authorized boot this could potentially trigger a medical review board. However if you want to proceed with this then get the documentation from your doctor.
Then you would need to write up a request for wavier and provide the specification for the boot you would want to wear. You can compare these specification against the boot requirements in DA PAM 670-1. Hopefully they match. If not you would need to explain the deficiency. After you have written your request for wavier you might want to run it by the JAG or IG for a review.
Then prior to submitting your request you would want to consider running it by your chain of command because it will become an official piece of correspondence to senior members of the military, specifically the Army G-1 office. Check with JAG to see if there is a previous precedence that could assist your request being approved.
See if your chain of command or the medical authority can support your request with letters of support or recommendation.
You could mail or email your request to the Proponent for AR 670-1 which is the Deputy Chief of Staff, Army, G-1

Who Do I Send My Request To?

If you look at page i of AR 670-1 it states: Proponent and exception authority. The proponent of this regulation is the Deputy Chief of Staff, G–1. The proponent has the authority to approve exceptions or waivers to this regulation that are consistent with controlling law and regulations. The proponent may delegate this approval authority, in writing, to a division chief within the proponent agency or its direct reporting unit or field operating agency in the grade of colonel or the civilian equivalent. Activities may request a waiver to this regulation by providing justification that includes a full analysis of the expected benefits and must include formal review by the activity’s senior legal officer. All waiver requests will be endorsed by the commander or senior leader of the requesting activity and forwarded through their higher headquarters to the policy proponent. Refer to AR 25-30 for specific guidance.

Understand the Potential Unintended Consequences of Your Request

As I stated previously I would make sure you fully understand the unintended consequences of such a request. The last thing you would want is to get a request like this denied and then be required to attend a medical review because you cannot wear any variant of approved military footwear. Check with the JAG and medical authority. Since you have an injury it may not be an issue. Do your research.

Thoughts to Consider:

My thoughts are you will need the support of the doctor with a strong recommendation along with strong recommendations from each Commander in your chain of command. Without this I am not sure G-1 will consider your request under Option 2. Another thing you need to consider is the structure of the boot you are asking to wear. How far out of regulation is it and why. In my opinion you will need to be able to explain this to receive a favorable answer.

What Should I Do?

I cannot tell you what you should do. I can provide some information for you to review and then you need to decide what course of action to take. I would strongly encourage you to do your research and in a professional & factual manner present your request to your Chain of Command and seek their support.