It may still be a problem. At the very least, when you get down to depth, you can still break off the fibers at that final depth. But, also at the very start, making your first passes, since this is end grain, not just cross grain, and the fibers are standing right on end, when you come across and break out the fibers, it may make a ragged edge in the vertical walls of the groove you plowed in the long grain because the fibers being broken pull out their brothers that they are stuck to. Sort of hard to explain. Whether you do long grain first or not, I’d suggest using a chisel to work the last bit of the groove so that the plow blade will never touch the final corner. You just need a tiny bit. It only takes a second to do. A file is probably fine, too.
This is a good reason for experimenting with scrap. 🙂
I’m sort of hoping that someone else has a magic way of doing this that is simpler.
Which reminds me….once you get below the surface, you may not need the saw kerfs. That’s a good thing to explore. You may only need to get, say, 1/16 to 1/8″ below the surface and then can just run the plow down to depth. Like I said, it has been too long since I did one of these. I don’t remember, and I think it depends upon how cranky the grain is.