Minor stropping without a serious abrasive simply lines the burr up with your edge rather than removing it. As Cliff mentioned this may be OK. If the burr is not too long or ragged and the steel is pretty sound it may do the job you want done without removing it. For shaving and light cutting this may be your most effective edge. If you work on something harder or more abrasive the edge may break down faster if you don't remove the burr.
As I got from razor manuals, stropping is not the answer when you work with ductile steels at low honing angles. That burr will move around, but not come off. If you get it to come off by heavy stropping you will tear the burr off which will not leave you a clean edge. The answer is to cut the burr off by very careful edge-forwards honing at a very high honing angle. You want a hone with a clean sharp surface. An ultra-fine diamond hone is best, but freshly cleaned medium grit Sharpmaker rods will work.
Here's how I would handle this with the Sharpmaker. Scrub your rods with hot water and sink cleanser, rinse. Put the medium rods in the "40-degree" (20-degree honing angle) slots in the Sharpmaker base, rotated to hone on the flats. Lay a D-cell flashlight battery on its side and use it as a fulcrum to support the center of the Sharpmaker base--like a teeter-totter. Tip the base to the right and lightly stroke on the right hand rod (which is now at around a 40-degree angle from vertical). Tip the base to the left and lightly stroke on the left hand rod. Repeat this process for only the minimum number of strokes to remove all trace of the burr. Use very light pressure and alternate left/right sides.
The next part of the process is to put on a true edge that is as thin as you want. I suspect that your freehand honing is giving you a more accute edge than you are getting with your standard Sharpmaker angles. So step one is to forget about using the "40-degree" setting. In fact, don't even use the "30-degree" setting on the Sharpmaker as-is. Move the medium rods into the "30-degree" slots, but rotate them to hone on the edges of the rods. Replace the battery fulcrum with a white Sharpmaker rod fulcrum. This time you are going to tip the base to the RIGHT and hone on the LEFT hand rod (which is now at under 10-degrees from vertical). Likewise you will tilt the base to the left and hone on the right hand rod. Use light pressure so that you don't bend the edge of the knife as you stroke the narrow edges of the rods. Only do about 10 strokes (5 per side) alternating left/right as you go. Do this the minimum number of strokes until the edge feels extremely sharp and slices paper effortlessly. Rotate the rods to use the flats and do about another 10 strokes using light pressure. Switch to the flats of the white rods (switch to using a medium rod as your fulcrum) and do another set of 10 light strokes. To give the edge a little more strength (and to compensate for a tendency for the edge to bend away from the rod as you hone) you want to finish honing at a higher angle. You could remove the fulcrum and just use the basic "30-degree" (15-degree honing angle) of the Sharpmaker. But humor me and try using a lower angle. Take one of the Sharpmaker brass guard rods and use it as a fulcrum under the center of the Sharpmaker base. Again you want to tilt-right/hone-left and tilt-left/hone-right, but you want to use almost zero pressure against the rods as you hone ever-so-gently. You do this maybe only 6 strokes (3 per side alternating). If you had some Spyderco Ultra-fine grit rods this would be the time to use them.
If you want you can very lightly strop after you are done.
PS, What alloy is this knife made from? The older Grecos were made from A2 which shouldn't give you so much of a problem. I think the newer ones are made from a saw blade alloy which may give you a burr challenge (at least that's what I've seen with L6 alloy).
