Paul, I did dye my own veneer. It's 1/16" thick maple. It's an area I want to explore more (dyeing thick veneer). I tried using a pressure cooker (as Patrice described somewhere), but that didn't seem to work very well. I'm sure I just don't know what I was doing with it. I ended up building a vacuum chamber and pulling vacuum on the veneer when it was in a bath of the dye. Used a ton of dye, quite expensive. I really want to experiment more with this, just hate listening to the vacuum pump all day.
You're right to be worried about tear out. I've had the edging blow huge chunks out when routing them in the past. These days, I flush it up by hand because of that. I just use a block plane or #4 hand plane to get the edges down close to flush, then finish up with a scraper if necessary. The nice thing about thick veneer is you don't destroy it so fast if the plane gets to it, compared to commercial thin veneer (which I've done).
I round the edges over with a block plane and smooth it out by hand with some sandpaper. Takes a little longer than a router, but far less risky. The less-than-perfectness of it give a less machine made feel to it, which I personally prefer.
That's a good idea. I think I'll round over a bunch of long strips, glue them on, and finish by hand.
The nerve wracking part will be when I cut the top off. My band saw isn't big enough so I'll end up having to make four cuts on the table saw with a good blade.