HandBrake

Just starting the process of compressing my library, which is almost exclusively 1080p action films generated from MakeMKV. I’m definitely passing through the highest quality audio tracks, but I also want to have a 2.0 track for my mobile devices. I did not keep any 2.0 audio tracks while using MakeMKV, so will need to encode the audio tracks available (mostly DTS-HD and Dolby True HD). I’ve done a TON of reading, and have read that the Handbrake default of AAC is not that great of quality...so my questions are:

What codes have you had success with when converting a high quality audio track down to 2.0?

Also, my library is mostly action blockbuster flicks. With that said, would it be wise to select “Film” for the encoder tune?

Depends on your playback environment. For maximum compatibility, AAC would be the best choice. MP3 would probably be next best for compatibility and gives good quality, but many players won't play MP3 when it's used in the MP4 container. Best quality would be FLAC (it's "lossless"), but then you have to be very selective about the player.

If you decide AAC is the best choice for you, you should consider using the nightly builds. The current nightly builds have a better AAC encoder.

The film tune is generally a good choice for film sources

Go with your highest quality 5.1 AAC as your only audio track, unless you are sure all of your devices handle native AC3.
In either case, the player decoder mixes down to perfect 2.0 for you, you can't do a better stereo mix manually.