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. 

Thanks Mesch. Yes it would be for cd playback and BD movies. Being it has optical input no reason not to use it with tv too.

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.  

Might get a more "analog sound" with the multi-bit version. I would save up a few more clams for that one if possible.

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.