Hi, JAS.
Welcome to LDO!
The donor screening process really can take quite a while, especially given under-funded programs and over-worked donor coordinators.
It definitely is possible for you and your scheduling needs to get lost in the system, at least temporarily. After a while, you may get a sense for what's the best way to work with your coordinator. E-mails may be more effective than phone calls, or vice-versa. Or, consider making friends with the secretary, who may be better equipped to focus on administrative, scheduling-type concerns.
I don't want to say anything definitive about which, if any, tests become obsolete at any given time (there are several others on this list who can be more authoritative on that) but I recall that, at my center, some of the more expensive tests were saved till after I had cleared several earlier (cheaper) hurdles first.
Like you, I had several tricky travel and work constraints, and I made it a point to remind the transplant center whenever I could.
Overall, you will need to be patient. As I have written here before, this process is a marathon, not a sprint!
Good luck, Snoopy