I keep my edges on the push cut level by touching them up on the Sharpmaker with the UF rods. Works even with a Global thinned to 10° and microbevel at approx. 15°.
Have you put your Birchwood through your stones? How long is your edge lasting? How much are you using/rotating/alternating at work? I re-etched mine after sharpening it a few times to get rid of the scratch marks.
The question is whether or not a more rounded edge is better for push cutting. After stropping you get a smoother edge, during the process you loose much of the bite. Jon told me that he doesn't like chrome oxide on a stropping pad because of the particles' shape, they are very round and take away most of the edges' bite.
If we are talking about ripe tomatoes, in my experience either you have a very toothy edge with much bite or a highly polished edge. something in between doesn't work well for me.
The edges do look very shinny with some bite on my fingernail and able to shave some arm hair. Do you use lighter pressure as you go up with in grit? Our on-vine tomatos were ripe, not very soft but ripe, our heirlooms were a bit soft.
It could be a dozen things.
I also doubt that fugi suji ever will.
I stop at 4000 with gyutos because I like the aforementioned toothier edge. Plus, I find them to be a little tougher.
The difference between try and triumph is a little "umph"! NO EXCUSES!!!!!!!