The two large beams I created, being about 11.5" apiece could fit through my planer. However, they are very heavy and I would certainly need some assistance feeding them through. I would like to say that my work ethic and commitment to traditional methodology prevented me from using the planer, but in fact it was a kind of impatience and laziness. I went ahead and joined the two hunks into the final 22 3/4" bench top.
I then realized how much work it would be to flatten the whole thing with a jack plane, so I got my 2.5 year old daughter to do it. I told her that it would be fun, and she believed me!
Once she had the top relatively flat (although quite scalloped since it is a jack plane) I was able to trim the ends. Again, I was tempted to use a circular saw but decided to use my coarse crosscut saw. It was way easier than I had thought, and did not take very long. Following the cutline was not a problem and the result is fairly square. It will need a tiny bit of truing once the bench is all assembled but not a lot. This is a good thing because trimming 4" of end grain doesn't sound all that fun.
Here's the top, at its final dimension of just over 4" thick, 22 3/4" wide, and 7' 6" long:
You can see that despite intentionally choosing the clearest wood possible, there are still a number of gnarly areas. Ignoring the very good wisdom of testing materials before implementation, I mixed up some epoxy and added food coloring, a bit of orange and a more substantial dose of brown, thinking it would look vaguely like juices from a fir tree. The result is more like something from a horror film, but it will mostly be planed away and hopefully not too bad:
Next I will flatten the bottom (since that is where the legs will attach) and build the legs. I've ordered vise hardware and now need to design the chop.