I populated the PCB this evening.  After re-seating the CP2102 with a little hot-air, it actually works.  Somehow the QFN package is a little finicky.  Maybe my PCB footprint is bad?  Anyway, here it is, before I solder the tin shield over the RF section:

I tested the USB connection on an old PC and through a lousy old USB hub that I don't care about.  Just in case. But nothing got fried :-(

Since the bias for the mixer diodes comes from the signal levels on the RTS and DTR lines, I didn't even have to write any software to test it.  I fired up gtkterm and used F7/F8 to toggle the control lines.  With DTR high and RTS low, the RF output is in-phase, while with DTR low and RTS high, the output is inverted, giving a 180-degree phase shift.  Or, maybe it's the other way around - it doesn't really matter for my purposes.

So far, I just tested it with the output of the DDS I happened to have on the bench at the time.  The 20 MHz output I used doesn't say much about the performance near 1 GHz, but at least the basics work.  Here's the input (yellow) and output (cyan) with the switch in one position:

and in the opposite:

There's a nice 180-degree shift between the two.

Although I don't need it for my application, you can also disable the output by setting DTR and RTS to the same value (although I suspect setting them both low might be best).  Here's what that looks like:

I don't know how much attenuation you really get in this case, but I'm not using it for anything anyway.