I think we all have tough beards and sensitive skin when we start shaving with a straight razor, then our blades get more efficient, our beard seems to get softer, and our skin less sensitive. It was the same way when I first started shaving. I can get more out of my edges between refreshing now, and quite honestly re-hone just for fun, experience, and maintaining the skill of it. Personally, I would use your free re-honing now or you'll wind up like me with 5 coupons in the drawer after you learn to hone your own. It sounds like you've eliminated beard prep as a variable, so why not continue to eliminate the edge as well by using the free re-honing, especially in the beginning.

Go with your gut, if you think it's the stropping, then it probably is, so do less and work up from there. In woodworking, you can also cut more wood off, but you can't put it back on very well. You can always strop lighter, with a more taught strop and for less laps. If that doesn't get your edge better than it was after honing or keep it the same between shaves, then start adding more laps on the strop. If you get to a ridiculous number then start messing with your strop tension then pressure.

When I look back at how I stropped in the beginning, I thought I was doing it right. Then I went to a meet and Glenn told me I wasn't using enough pressure. After using more pressure, I was able to maintain my edges longer between refreshes. Then somewhere in there, I started to add too much pressure on the spine and the edge and was having to refresh more often. Now, I find that I add a light to medium pressure on the strop with the spine, and I use enough tension that the strop deflects just enough to hit the edge, but I just let the edge follow the spine and kiss the strop (so light pressure on the edge). That's what seems to work for me.

Hope this helps!