Honestly... yeah, that's expected. Modern mobos have pretty good DACs in them these days. It's not possible for you to be getting the onboard output through an external DAC. That is how it sounds, and if there's a noticeable quality issue that is unchanging between the DACs you've used and the onboard, it's somewhere else in the chain. The DAC probably isn't your bottleneck.
That would be my real question for you here. What issue lead to you getting the DAC? If the only problem is really just down to not noticing an increase in quality, then a DAC is never gonna be the answer. I'm not familiar with those speakers, but from what I see they're your standard powered nearfields with a nice bonus having the sub with the amp integrated in... a lot like some Polk bookshelf kits I've seen. Should be pretty good to go with that setup. All I can really say is that there are some pretty significant limits on what speakers in the class can really do. A lot of the time, with nearfields in this price range, the weakness is the amplification itself... not so much in terms of power, but in distortion. They aren't the cleanest things. Tend to be pretty spartan plate amps.
JBL puts some pretty serious design tech into even their lower-end speakers. They're one of the biggest brands in professional audio. The 3-series that everyone knows for the LSR305's even gets that fancy diffusion stuff that goes on their high-end demoing and mastering speakers. And it works. But the amps in those LSR's are TRASH. Seriously, they are basic in design and componentry, and measure horribly. And while they don't sound bad at all, there are limits to how loud they can go before that distortion catches up and has them getting harsh. And obviously they do not have the detail of real, high-end studio monitors. I have them, and for years I've thought they sounded great, but they do still leave a lot on the table.
So that's part of the game, too. At this price, or really any price... but especially this one, the main limiting factor in sound quality is in the speakers themselves. Outside of that, you might consider messing around with the placement - it really is a pretty big deal with this kind of speaker... especially being that they typically wind up in bedrooms... acoustically perilous places. A desk is also about the worst thing for good sound. But I bet you're using one. As am I. Simply by placing them on a desk, even on 'isolating' desk stands, you have compromised more of the sound than the cheapest working DAC you can buy right now would. The surface of the desk still bounces all of the sound coming straight out of the speakers. Dealing with reflections is the number one difference-maker with any speaker setup. Everything else outside of a suitably powered amp is just money you could've spent on better speakers.
