Hey…I wasn’t taking anything personal. 
I was doing some looking around and I see you’ve been at this for quite some time…here…like 2009 or something.
I found a reference on that help2hear site about pinouts as well that might be of interest if it isn’t already old news to you. Although I don’t know how to check them in this case.
I would vote the gender changer to keep it simple and fewer cables. The iogear seems to say it’s already null modem. Although so did the Startech.
With other looking I did, I found that the chipset of these adapters may have something to do with it. That Startech one is ftdi. This iogear suggested by GN themselves is Prolific. Somebody claims success with the Belkin F5U409 and it uses a Philips chipset. And they went somewhere else for an updated driver. So who knows.
Dang! I feel your frustration. It’s extremely puzzling that it works for programming but not firmware updates.