First of all - my apologies. I am still getting used to the new look of the website and I'm finding it hard to locate new posts or comments. I'm sorry you had to wait so long for a response from me!
As for your question, the simple answer is that your employer does not have to give you the desk job as an accommodation if it is considered a promotion. Under the Americans with Disabilities Act (ADA), employers only have to consider reassignment as a reasonable accommodation for positions that are vacant and equal to or less than your current position in terms of status, pay, etc. If it is an equal or lesser position, your employer may have to consider you for the position as a reasonable accommodation if you request it as such.
The more complicated answer is it depends. Reassignment as a reasonable accommodation is considered the accommodation of last resort, meaning you and your employer should first consider whether there are accommodations that can assist you in keeping your current position. It sounds like you are already doing some self-accommodation, and perhaps it is time to look at whether there are some more formal accommodations that could help you in your current position.
However, that only addresses the "disability" piece of the situation, so to speak. You can still apply for the position without requesting it as an accommodation. I can understand your fears that your employer may not be willing to consider you for the position because you are needed in the position you already have. Regardless of whether you apply for the position competitively or request it as an accommodation or do both (some employers still require one to compete for open positions even when they are being requested as an accommodation), you should be prepared to discuss why you will be of value to the company in the new position to show your employer why this would be of benefit for them as well as you.
Here is some information on accommodations in case that is a new topic for you:
The Win-Win Approach to Reasonable Accommodations
Employees' Practical Guide to Negotiating and Requesting Reasonable Accommodations Under the Americans with Disabilities Act (ADA)
The ADA: Your Employment Rights as an Individual with a Disability
Finally, if you would like to see whether there are possible accommodations for your current position, I encourage you to give the Job Accommodation Network a call to see what types of accommodations have worked for others with similar positions.
Best wishes to you!