There are a couple ways Al !!!!!! Depends how much time you have or how much time you want to spend.....From the looks of the pics the seams, or ends seem very cleanly cut, and clear. Are there are any saw marks on the ends or did you run your pieces through a jointer or clean the ends up with a router w/straight bit first?
My way is long and tedious. I run all my edges through the jointer before gluing and assembly. Once everything is assembled you have that bit of a hang over, and I take a straight bit in my router and trim it all flush. Usually I put a mark somehow on the end of the work piece where I start the router in at, and that's when I go back depending on the severity of the mark/gouge, and use regular sand paper to smooth it out. Then I step up to wet sanding all my edges by hand with a little sanding block. Very tedious, and I work my way up through the grits of wet/dry sandpaper till they are super smooth and almost clear. Then I start with the micro mesh polishing.......I continue that till they are like ice cubes.
Another thing I have done in the past is use Novus polish. They have 3 different grits....It's a small bottle you can find the stuff on Ebay, or your supplier probably has some laying around, but usually I start with Novus 2 and work my way down....I only use 3 if the scratches are super bad, and using the Novus is a hand finishing as well, and takes time.
If I'm in a super hurry and rush, and don't like doing it, because it can cause stress to the material, but it is done all the time.....FLAME POLISHING !!!!!!!
Sounds a little scary, but actually with a little practice it's super easy......Depending on the tools you have handy makes the job easier.....Here at the house I don't have a torch set. Oxygen/Acetolene (spelling), but you don't want to use the big heating torch tip. You'd want to use the real fine small torch tip, so you can work precisely. Another way around the torch is issue is to use the standard blow torch. If I do flame polish, I prefer to use MAPP gas vs. Propane gas......MAPP is hotter, which means I get a nice flame, and keep the torch moving along the seam, and don't bubble the seam/joint. Again probably easier to use MAPP IMHO, since it burns hotter.
What you would actually do is adjust your flame to where the flame is blue, not orange, and you want to start at on end of the seam(exposed edge), and draw the flame along/down the seam.....I like to get the tip of the flame just off of the work piece. A big key is to keep the flame moving....You hold it to long in a spot, and you will here things sizzle and sound like bacon......Then your work piece edge will bubble up.....Then you go back to hand sanding to work out the damage.....Another key here is to NOT overheat the seam/joint. If you hit the seam/joint, go only once, and then on to the next seam. The key is to not put undo heat/stress to any joint or edge. After you have made a pass on all the seams/joints, I usually take a smoke break, and let the piece cool....Actually the material isn't hot, but I try not to warm the material very much. I gauge my progress during my break checking the look of the seam/joint, and if needed go back and hit the joint/seam that needs more attention. Again 1 pass and don't overheat or hold the flame in 1 spot. It's easier to go back with quick passes, than rush and overheat a seam......
Hope this helps you out Al.....I
f anyone wants I could try to put together a quick video of flame polishing.......Another key is DO NOT Flame polish your edges and such first and then glue......Glue first and then polish......