If my wish was for a 975 but with 2 HDMI outputs (vs. the 1 that it has) would combining this with the HDS-42AVR solve that? I would not be using a 4K/UHD television (which is a use for which it is being touted).

The short answer is no. You would still have to split the same HDMI signal to the HDS42 and to the 975.
An HDMI splitter could be used at the 975s HDMI out.
I haven't tried any of these, so I can't recommend any, Don't know how well they work, or if there would be handshaking issues. Maybe someone else could offer their experiences.

12Stepper - What are your trying to use the 2nd HDMI output for? If the answer is to send a single source to two different monitors the answer is probably no. You would need an HDMI splitter for that. If your objective is to get a single additional hdmi video source to the 975 and out to your TV, then the answer is yes and you can use the 975's Aux configuration for that). If you want to use analog video instead of digital for some of the 5 975 input devices that can also be accomplished. If you are looking for more than 5 and less than 8 video inputs then the answer is probably yes but it is certainly not user friendly and requires manually switching of the HDS-42AVR's input.

The reason, I am sure that this will work is that per the standard configuration, there are two HDMI lines going to the TV: 1) the passthrough output from the HDS-42AVR which will switch up to 4 HDMI sources and 2) the 975's HDMI Output/ARC input. Per the manual at a minimum the ARC line is used for 975 console settings. In my case I have HDMI 1 on the TV connected to the HDS-42AVR and HDMI 2 connected to the ARC line. The ARC line can send digital and analog video input to the TV (analog works through the 975's autoscale feature).

As background to the above, I recently purchased and installed a TE HDS-42AVR from Outlaw to fix a communication problem between my 975 and Plasma TV that resulted from an electrical hiccup. After the incident the 975 would not send a signal to the Plasma or conversely the Plasma would not accept a signal from the 975. Both worked fine with other devices including a cheap 32" Visio TV. I could also manually connect my source devices to my TV's HDMI 1 input and the HDMI 2 ARC to the 975 and get audio on the 975. While this solved my needs, I wasn't comfortable asking my wife and kids to switch HDMI cables on a regular basis. I tried replacing the computer and HDMI combo board on my Panasonic Plasma which should have worked but didn't (bye-bye at least $200 in labor plus a restocking fee on a $400 board).

Various manual procedural fixes suggested by Outlaw and Transformative Engineering also failed. Finally, Jason from TE suggested I try the HDS-42AVR from Outlaw as the cheapest and best solution. It fixed the problem.