I can't vouch for it working but this mob have been around for some time.
Latest email here - has two inputs and one output. Main website here
They've got lots of different models. ($100 - $200) You can write and tell them your requirements and they will recommend a best match.
I bought one off them for my dad a few years ago (TV didn't have HDMI inputs) and its worked well.
I'm not sure that paying for streaming (subscription plus data) is comparable with watching it on FTA TV. For sure Olympics coverage is always tricky with so many events running simultaneously and often at odd hours of the day and night, that's the true worth of a good program manager with their hand on the pulse of what their viewers want to watch at any point in time. Undeniably Channel 7 were devoid of such skill and experience. Foxtel, for which I paid nothing extra, had 8 channels for the 2012 Olympics and Seven had 3 at best, with Seven and Seven HD showing the same content. Often 4 HD Channels versus 1 HD channel this year.
Next Olympics I am confident that I won't be alone in watching next to none of it on FTA or PayTV. The effect of that on their revenue stream will be devastating, not sure how they sell advertising when so few will be watching, with "add blocking via Firefox" just another nail in the coffin. Personally I would not be surprised to see no one bid for the Australian broadcasting rights.