Will budget Schiit Modi3 help?

Any possible improvement would be dependent on the rest of your system. 

The improvement would likely be greatest when outputting CD playback from BD player via coax SPDIF.  Not sure about improvement from TV over the FiiO DAC3. 

Schiit has 15 day return policy. You lose shipping cost only.

For under $30, I would give it a try. If you do so please let know your thoughts. 

Yes, no reason not to use it for both sources. Just that improvement will likely be different depending on source. 

I own the Yahame BD-681. It has selection for CD playback, removing video in path. If your model is similar, it might prove out that using the DAC for music and the analog out for BD movies might prove most advantageous.  

The Modi3 sells for $99, the multi-bit version for $249. Quite a substantial % increase. Not to say it isn't worth it, that would depend on intended use and funds available. 

Great, let us know how it proves out for you. I do have a Modi 2, which is USB only. I use it to stream from my computer. 

Glad to hear the Modi is working out for you. Nice B-day present from your wife.