I called Dynon support this afternoon and resolved the problem. Getting the SL-40 talking properly involves two configurations settings:
1) Configure Serial Port 4 RX, selecting the Apollo/Garmin SL-40 on the pulldown menu (this I was doing)
2) Back up a menu or two, and select "DISPLAY COM" or something like that, where you then select the SL-40 (the default is none).
This then puts the active and standby frequencies on the top bar on the Skyview, and when in an Airport's INFO--COM screens, makes the push-to-com button appear on the bottom (APT>COM??), the pushing of which will load the selected frequency into the standby on the SL-40 (unless it is already the active frequency).
The other mystery solved by this was why the TX count in the Serial Port Configuration Status screen remains at zero while the RX count continually increments. The SL-40 will continually send status on its Serial Out port, while the Skyview will only send when you manually push the frequency to the SL-40. I could only push things when I had the SL-40 selected as the com to display, such that the magic button appears.
Now that I know how to do it, I guess I'll have to re-read the destructions, and see if these two steps are really documented or not.
The Dynon phone support folks are very helpful.