I hate to say it, because it's a truism. You can have any practice style that you want, it just depends on what you are willing to sacrifice to get it.
There are some surgeons outside of the bigger academic centers who do kidneys, I am not aware of any that do livers. They are transplant trained and also do some general surgery and generally operate at community teaching hospitals. You can find listings of all transplant centers
at
http://www.ustransplant.org/csr_0105/index.php
Still, the biggest job opportunities at at academic centers that you would at least recognize their names even if they didn't spring to mind as a "big-time" center. They are spread out all over the country.
Research and scheduling is determined by your group both in size and composition. Academics tend to negotiate for some research time off either by days of the week, weeks of the month, or months of the year. However, the ability to do this is decreasing as academic centers rely more heavily on their clinical revenues than ever before. The size of your group probably matter more. The reason I say this is that every center has a waitlist. As a transplant surgeon you generally get a call from the OPO (organ procurement organization) coordinator with an offer of an organ from a non-living donor and you can say yes or no. You can give basically any reason for saying no, but in the back of your mind you know this patient who is waiting for the organ and it is difficult to say no if the offered organ is a good one. A big group is able to rotate the call in such a way that you don't have to be on organ call all the time.
Finally, WHAT organs you choose to make part of your transplant practice makes a difference. If you only do kidneys (which many people do if they aren't in a big center. Some fellowships only train you to do kidneys.
http://www.asts.org/fellowshiptraining.cfm ) your life is actually pretty good. Most kidney will last a long time on ice and you can schedule them for a time that is somewhat convenient for you (i.e. not at 2AM). The operation takes about 2-3 hrs from lines in to skin closed. Many can be scheduled because there are living donors willing to donate. Most receipients leave the hospital within 3 days. If you do pancreas and liver then you are working against the clock a little more, as they don't last as long on ice and they stay in the hospital a lot longer.
Pay averages a lot better than general surgeons as a rule since the operations pay better and the donor operations pay really well (they are cash-pay via the OPO). Last time I looked in the AAMC book I seem to remember about a 30-40% premium for transplant surgeons on average level for level (e.g. assistant prof to assistant prof.) as compared to general surgery.
I hope that helps.