Heya,
Well, what's your maximum limit on the budget then?
I'm of the mind that you should spend most of your budget on your headphones, then make sure you have a good source (lossless audio) and then make sure your DAC is worthy of feeding your headphones, finally, the amp last. You spent more on your amp than your headphones, I wager. They retail about the same cost, but you can get HD598's in the $180 range, while the Asgard runs $250 usually (unless you got it used, around $200).
And now you're talking about getting a $350 Bitfrost DAC. It's likely to be an incredible DAC, but you're paying more than your headphones for it, which is odd. That's something that people with top end flagship material do.
For the budget person, who doesn't want to spend $350, I'm surprised you picked up the headphones you did, but you're willing to spend nearly three times the headphones' cost for your amp/dac combination.
Well, I'll get off the soap box now. You have what you have and hopefully love it. Let's get you a source.
I'm going to suggest a super cheap solution and then the more modest solution.
Cheap - Check out the FiiO D3. It's $30. It's DAC chipset is quite good. It is cheap, but that doesn't mean it doesn't perform well. It accepts optical input and then outputs to your amp. Does exactly what you need. And if you don't like it or it doesn't do what you need, $30 isn't a huge loss. I bet if you put it up against the HRT Music Streamer II and blind test, you'd be hard pressed to actually pick them apart in most applications.
Decent - HRT Music Streamer II is quite good for a USB DAC. Yea, you're not outputting via optical, but that doesn't really matter. It's USB allows for what's needed and is excellent. Does what you need. Unfortunately as USB only, it only works from a computer unlike other DACs that can take inputs from several devices should your equipment collection grow. This is a DAC you outgrow depending on your sources in the future.
Modest - Matrix Cube DAC. It's $270 shipped. It accepts all kinds of inputs, USB, optical, SPDIFF, etc. It's a good DAC, but also has a pretty good amplifier. It allows you to upscale everything to 24bit/192khz. It also allows you to monitor via it's amplifier and from your external amplifier, so you effectively get to have two headphones running if you wish (I love that because I do a lot of swapping headphones based on what I'm listening to and don't like to always pull cables, I like just putting on another pair that are already playing). Or you step up to the Bitfrost for nearly $100 more and get the same effect, minus the dual listening from the secondary amplifier. Plus it's flavor of the month, so everyone will recommend it.
Very best,
