I find it hard to believe that the laptops must run on battery only, must run for 12 hours straight and that the only workable setup is these Fujitsu machines with removable batteries and the ability to run a spare battery in the battery bay (not required, but sounds like even that is favorable here)
The reason I find that hard to believe is that is it really a situation where these machines move around ALL DAY LONG? Each employee carries their own with them from room to room? The machines do not stay in the room, so a machine goes with a doctor where ever they go? It's rare that I've ever seen a setup in which a desktop computer isn't sitting in each office, and when it isn't it's a laptop that is still plugged into the wall.
If these tablets really are on the go 100% of the time, and have no time ever to be charged, then I guess what your already providing is pretty much the only available choice. If these machines are not on the go 100% of the time, then I do not see a reason for it to be this way.
In my experience with doctors visits of any kind, if I'm with the doctor for half an hour, they spend about 5% of that time with the computer. The rest of it, it sits on a desk while they are working with me. At any rate, you've decided what is best for your client based on your walkthrough. I just take a bit of a different attitude when I'm not the expert. I can go into a garage asking a mechanic for an oil change because I believe that's what it needs, and when the garage tells me I need to have the front and rear ends serviced I don't refuse (mainly because my mechanic is my father, who's been doing it for 30 years) because he knows far better than I what my vehicle needs and if or not my google fu answers are reasonable or probable at fixing whatever problem I may have. Sometimes my google fu lands me pretty close, if not right on what's wrong... other times if not for the knowledge and experience my mechanic has I'd have had one hell of a rough go getting things sorted out. Same here. It's not wrong to tell your clients they are wrong, if they are wrong. Most of us are not in a habit of taking their assessment of their needs as correct. Especially if it's a client that we need too or intend to support long term.
But it sounds like your all figured out. I learned something too, I didn't realize such a hardware setup existed any more. I can't think of any direct use cases right now for anyone I do work for, but it's an option I now know about!