As HDMI can pass 8-channels (7.1) of PCM (uncompressed) audio, there is no real reason for using audio compression (DDL) with HDMI.
Not even sure if your TVs can output 5.1 compressed audio, the TV might only output 2-channel PCM thru the optical output.
Just get an Asus Xonar DG or DGX sound card for your computer, the DG(X) will output Dolby Headphone surround sound, to headphones, just like the Mix-amp.
So no need to output audio from the TV or have to use the Mix-amp.
Just switch the audio output (Windows control panel>Sound>Playback) from the Xonar DG(X) to the HMDI out when you want to send audio to the TV, from the computer.
I'm using a gaming mini ITX built, with no room for a dedicated sound card. The onboard sound is Realtek ALC898, which Asus says it supports DTS Connect, but no mention of DDL. On the other hand, the Realtek specs for ALC898 says it supports both formats, DTSc and DDL, but it depends on the mobo maker to implement it (i.e. pay for licenses).
And besides, i also have a console, and something like Mixamp would help me use Dolby Headphone for it too. Most probably i won't get the Mixamp, and go for something like the Audio Technica DWL3300 system and use my own headphones. But i still need DDL & DTSc on the source, in order to work correctly.
About the TV, do you mean the TV should have DDL encoding for the optical output?