Welcome to FT,
taterman!
You won't have any luck talking your way into an upgrade with United due to your injury, or any other reason really. You could see if an Economy Plus seat is available to purchase which offers at least a few more inches of legroom. I don't know what the rate is for that route but if you log in to the UA website and select that itinerary, then go to change seats, it will show you the price. The cost for buying an E+ seat wouldn't normally be reimbursable on your travel voucher.
It is possible to get authorization to purchase a business class seat if your Authorizing Official (AO) approves based on the facts of the situation. Not sure if you're working for a civilian agency or DoD, but this FTR section details the criteria (I only cited a portion below)
http://www.gsa.gov/portal/ext/public...868/#wp1088868
§301-10.123 When may I use other than coach-class airline accommodations?
Government travelers are required to exercise the same care in incurring expenses that a prudent person would exercise if traveling on personal business when making official travel arrangements, and therefore, should consider the least expensive class of travel that meets their needs. You may use the lowest other than coach-class airline accommodations only when your agency specifically authorizes/approves such use as specified in paragraphs (a) and (b) of this section.
(a) Your agency may authorize/approve first class accommodations if any of the following apply:
(1) No coach-class accommodations are reasonably available. “Reasonably available” means available on an airline that is scheduled to leave within 24 hours of your proposed departure time, or scheduled to arrive within 24 hours of your proposed arrival time;
(2) When use of other than coach-class is necessary to accommodate a medical disability or other special need...
Whether or not your condition would warrant and your organization could fund the cost of business class is something you'd have to discuss with your AO.