That's a bummer. After all, I'm cutting my fullers with an angle grinder right nowand as a consequence, have found this thread very interesting. What if you cut in the fuller to the length of the table, and then just reclamp the blade in a different position and cut in the rest? Would that work? I have never used a milling machine before, so pardon the noob question. I'm just full of those today.
The only reliable way I can think of is to build a clamping fixture with stops or a lip that you can set the stock against so that you are sure it is in the same cross position every time you clamp it. Also, you'd pretty much have to mill the fullers in first, before profiling the blade at all, so that there is a nice square edge to line up on the fixture.
You'd still want to sweep an indicator from the spindle to the stock every time you re clamp just to be sure, but it would probably work just fine.
The biggest problem with using a Sherline for this is that the machine is so small that having a sword length piece of stock hanging off one edge of the table might put a meaningful torque on it. I'd want to have at least a 14" horizontal travel square column mill for sword fuller type work.
Going up a size of mill opens up a lot of new worlds as well, such as gunsmithing.