[DesertRatTom]

Do you have a shoulder plane? If so you can get down close, then use the plane to get the thickness exactly right. Another thing I would consider doing is using a japanese pull saw to do the crosscut pretty much to depth, then use the router. That should eliminate any tearout since the bit won't have to touch the shoulder. I'd use that shoulder plane to creep up on the fit. If you're going to use glue, that's one thing, but if you want to break down or move the bedframe, you should consider a couple of pegs that you can push out to move the thing. Eventually, it will have to be broken down, so I just wouldn't use glue. My take on this anyhow.

 

[DesertRatTom]

Using a shoulder plane makes it pretty easy to get a nice fit. Get it close with the saw and router, then take a stroke or two with the plane, then repeat the exact same number of strokes on the other side. The setting on the blade determines how much you shave off on each stroke and that can be very thin, so it is easy to shave, trial fit, shave until it's just right. See pix.

The japanese saw cuts on the pull stroke and is razor sharp so you cut down to your mark, route the bulk as described, then use the plane. A shoulder plane cuts the full width of the plane. A Japanese plane cuts on the pull stroke, which is easier, but can not cut all the way to the shoulder, you will have to go back and use a chisel for that. Note the stiffener on the back edge of the saw in pix.

Theoretically, you could use a wide chisel to fit the tenon, but it requires very careful work and is much easier to overdo than with a shoulder plane. Just FIY, I added a pix of a wooden Japanese pull type plane.

 

[DesertRatTom]

I found a cheap shoulder plane on Amazon and happily, it wasn't too far off. Using sandpaper of various grits, I flattened the base and made sure it was 90 to the sides, then carefully sharpened the blade. I spent maybe $40 for it. I use it fairly often. It is 3/4 inches wide so it is perfect for perfecting rabbets and tennons, and I have salvaged a couple of $50 picture frames where I made an error on the front profile. The front of the cheap plane comes off which turns it into a chisel plane, which is far easier to control than a straight chisel. I must add that using a hand plane is very addictive. You quickly come to understand how such wonderful work was done in wood before the advent of power tools.

 

[DesertRatTom]

Being in the instructional mode, here is a pix of a router plane. Beyond being beautiful tool, it is really good at flattening and perfecting the bottom of a dado or groove. It must have support on both sides to work properly so it isn't good for tennons or rabbets. It is also great for inlays where you want a shallow, but exact depth of cut.