You should be able to keep your convex Reeve edge on a Sebenza by using the Sharpmaker, with some care.
But taking a normal, flat grind at the final edge and getting it convex is going to take a bit of work.
Here is a Half-fast (get it?) way to do convex with a sharpening jig (Lansky, Gatco, EdgePro):
Start with a very shallow angle. On the Lansky that means 17 degrees. Fully bevel the edge this way. Then go to 20 degrees. At this stage you have a double beveled edge. Then put a final edge on with 25 degrees. This is going to work best on a flat ground blade (AFCK, Military). Like I said, it ain't a pretty convex edge, but it is part way there.
Cliff Stamp offered the following technique for resharpening a convex blade for those of us without belt grinders that can be run "slack"... you basically need a soft backing with abrasive on top. Cliff said a thick piece of leather (say, 3" wide by 12-14" long) would do it.
Here's how I chose to do it:
Bought a very flat, straight 2"x4" at Home Depot (forgot the grade... finish grade?). I used a 14" length of said board. Found an old computer mouse pad that had a neoprene backing. Cut neoprene to size and glued onto the 2x4, rubber side up.
When I want to freshen up a convex edge on say a large blade, I put 400 grit wet or dry autobody sandpaper (Pep Boys, Auto Zone, etc) on the rubber, one end of the paper under the 2x4 to hold it steady (glued some square pieces of mouse pad to base as no-slip feet). I put the knife on the paper and pull it towards me, like I'm stropping the edge (not cutting into the paper, the opposite, pulling edge along paper). The soft neoprene backing will conform to the blade shape (if already convex, it conforms) and with some care and just a bit of practice (I had no trouble first time), resharpen the convex edge.
I believe you could, with care and practice, create a half-fast to a decent convex edge by kind of rolling the spine upwards towards your chin as you pull the blade towards you on above "sharpener".
Or, go to Sears or something and buy a small belt sander ($200+) that can run the belt slack and do it that way. Start with fine grit... 600 or so, so you don't do any damage while learning. 400 works with the "strop" approach for me.
I also have a bench grinder set up to sharpen my big beater/user knives and machetes. Two hard fiber board wheels...one with silicon carbide grit glued to it for taking metal off, the other with fine rouge for removing the burr. bought the wheels from Melvin Dunn. Texas Knifemakers Supply sells them too for $20. See this link and look under "sharpening equipment, page 1":
http://www.texasknife.com/store/s-pages/TKS_MainframeStore.htm
This takes practice... I can get a shavin' edge on my machetes (cheap ones) even at a relatively steep 25-30 degree angle, but they are uneven in terms of grind angle as it's hard to pull 18-22" machetes across consistently when you are an amateur. However, this approach on a bench grinder, after stropping off the burr with the rouge wheel, tends to produce a convex edge also. Practice on cheap stuff! Ontario machetes and the like recommended.
