I would shoot multiple images at one minute intervals and then overlay them in software. With a digital camera, if you have the sensor going for that long, you're going to generate so much heat and noise that the picture is going to look pretty ugly. Astrophotographers will sometimes get around this by building special liquid cooling units to draw the heat off of their sensors to reduce noise, but that would be pretty expensive for such a simple project.
When you go to combine them in software, don't try to combine them all at once. Just combine a few at a time, render that down into a single image, and then once you have a bunch of them, combine a few of them and render them into a single image, and so one until you get all of them together on one image. If you try to do them all at once, you'll likely lock up the computer and crash it.
I've actually done this, though I used film. I used a large format camera to do this, which allowed me to stop my aperture down quite a bit without having to worry about diffraction. And instead of using just an ND filter, I used a red, green, and blue filter (plus and ND) and recorded the image on B&W film. I then combined them in the print stage to create cyan, magenta, yellow, and black separations for a 4-color process image. By using slow film in a low light environment, and colored filters, I was able to make exposures that were several minutes long each, without having to worry about sensor noise. Reciprocity failure actually played to my benefit here. I actually took that photo over the course of several weeks, allowing several days to pass between each exposure, to get the flowers in the vase to die. I have a digital render of the scanned negatives of it looks quite a bit more detailed, but that's buried in my computer somewhere deep, and I don't feel like looking for it. I do, however, have this scan of a Gum Bichromate that I made from it (my second gum print, so I didn't exactly do a great job on it), but while it lacks the detail and precision, it does give you a rough idea of what I'm talking about.