Since Vanderbilt is a top hospital, I imagine they would have at least one patient advocate there. You might try contacting one and expressing your concerns about not being seen until 01/16. I imagine Vanderbilt books up well in advance, and that 5 weeks away is not so bad. However, if your husband is that weak it would seem that it would be prudent to have him evaluated ASAP, and the testing for live donor to be done quickly. All I really know about that is they need to be the same blood type...I think. (To those who might know: Since O+ is a "universal donor," would it be considered doable if the son were an O+ and the dad is a B+?)
My concern would be that in waiting that long, your husband may become too ill to undergo surgery. However, in the case of transplant, perhaps it would be a plus. Someone who has had one or been the caretaker of a transplant patient can provide more info than I.