When I got the whole thing glued up it was not flat so I decided to flatten it using the end of a router bit (in the router table) to essentially fly cut it. I tried out the technique on some scraps and got a finish on the end grain that was absolutely silky. When I was making these trial cuts I was holding the scrap freehand and so I went really slowly. Having convinced myself that I knew what I was doing, I proceeded to do the cutting board.
You have proceeded logically. the only error you made was in not doing your final piece in _exactly_ the same way as your test piece. That said, you did not "test" your test piece adequately else it would have shown a variation in thickness.
I didn't have a pair of skis so I clamped two end pieces to the cutting board so that when I had done the whole cutting board it would still be supported by those pieces above the cutter. Think inverted ski setup.
That is logical and your hypothesis is sound.
The maximum cut that I took was less than 1/16th. I worked my way across the whole board pushing each pass with a miter kind of like mowing the lawn. Got done and flipped it over eager to see a silky finish.
Silky? Hardly! Really really rough would be more like it.
There is an additional option. When I'm doing rabbets etc. it is very difficult to keep a large bit perfectly perpendicular to the table. Cheap bits will also have one "edge" slightly lower than the other so you may also get a roughness in the cut that way. I've found that plunge routers are more susceptible than fixed base with the full sized adjusting ring to the "vertically challenged conundrum."
I finally figured out that when I was pushing with the miter I must have pushed a lot faster. To check that as the cause I tried another test piece in exactly that way and sure enough it is just as bad as my cutting board. Arrrgggg! I had no idea it would be so sensitive to feed rate. Feed at a snail's pace and get silky finish, feed faster and get nasty rough endgrain surface.
This is more telling of a cheap bit than one can think. You push the router more aggressively, the bit hasn't time to "clean up after itself" so the surface seems rougher.
For my next round (I do think these cutting boards make fantastic gifts) I will build a pair of skis so I can see what I'm doing and get feedback along the way.
That will help but if you use the same bit, you may wind up with the same problem. I would also suggest you learn how to sharpen and use a cabinet scraper. The skis can even the surface out for you and the cabinet scraper will give it that "sheen" you seek.
With that background, let me pose a question: When smoothing endgrain with a router bit, can any of you give me specific tips on bit size and speed? Naturally the larger the bit the less passes I will need to make. Any downside to a larger flat bottomed bit? Also, is there a rule of thumb for cutter speed for end grain that is different from side grain? I know there will be a calculation to get the speed of the cutting edge as a function of bit radius and router speed so perhaps the key parameter is the speed of the cutting surface (bit radius x router rpm x 2pi/60 x 1/12 should give feet per second at the outer surface of the bit).
A large bit and a small bit each suffer their own limitations. A small diameter bit needs many passes but can remove more depth per pass. A large bit removes less depth but a greater diameter and thus requires more passes. Your best bet is to use what your router is comfortable working with and finish with a cabinet scraper. If you check on the packaging that comes with your bit, there should be some indication of the speed it requires.
Learn to listen to your router. It will talk to you and tell you what it needs. You want to keep the song as high pitched as possible and still working. Don't stop the bit but don't let the pitch drop an octave (in musical terms.) For the bigger bits, make sure you're using a full >3 HP production router at the slowest speed setting. The Hitachi M12V or the Makita 3612C are both excellent for this type of work.
Cabinet scrapers can be found at LeeValley (for reference) and many finer woodworking stockists.