If however, you have something similar to an ASUS Xonar and it's ilk, then you won't need to use ALchemy.
The DirectSound3D components added to the drivers of these cards will do that job for you.
(As such, I've had rather lovely accelerated audio ever since I bought the original Sins.)

ALchemy only works for Creative Audio hardware, or 3rd party hardware using Creative chipsets.

That's exactly what I'm saying, the drivers for these cards provide full accelerated audio for pretty much every game that supports it, even with EAX games.

DirectSound3D GX is as far as I'm aware unique to the drivers for the CMedia chipsets used in these types of cards.

To quote the manufacturer:

DirectSound3D GX translates DirectSound calls (ie. stuff that would normally call the hardware directly in XP) to the software level where the drivers for the card can take over. True hardware accelerated audio doesn't exist for Vista and Windows 7, even ALchemy is a mere facsimile of that.  The Xonar D2X I have does most of it's normal processing in software, but it does hardware encoding of that to Dolby Digital Live or DTS so I still get full hardware 3D audio. It also has limited X-Fi support (it can do up to EAX 2.0 in software and emulates it up to 5.0).

The biggest difference with the Creative solution is that DS3D GX doesn't need to be modified for each game, it intercepts the normal calls and makes them usable again, something that does need to be done for ALchemy. If a game isn't in ALchemy's definition list, the software does nothing for the game. 

So far, every game I've played that can do surround sound, has done so, with awesome fidelity.
And because of the real-time Dolby/DTS encoding you can also get 3D audio through the SPDIF connectors, which is handy when you hook it up to a receiver like I have. No more 2-channel only PCM audio.

Well, the ASUS Xonar D2X I have gives me some of the benefits you mentioned.

128 sound channels are possible (it's mentioned in the specs in the manual) and real-time dynamic sound processing is done on the card by the CMedia chipset (which has hardware EAX 2.0 and emulates up to EAX 5.0). 

the basic stuff however is still done entirely in software on the CPU, so there's no CPU load reduction as such, but most modern PCs aren't exactly CPU limited anyway.

Besides the EAX stuff the only other thing the card does is encode all audio output into either Dolby Digital Live or DTS in real-time. This encoded audio-stream can then be fed to a receiver through the SPDIF connectors on the card to provide great surround sound. Without it, SPDIF is limited to PCM audio only which is 2.0 only, rather than up to 7.1.

Most newer games have audio encoded in either Dolby Digital or DTS already, so the card only needs to pass it on, but for older games that real-time encoding is rather handy. This is of course not needed if you're using the 7.1 analog output the card also has.

As for the headphone stuff you mention, the Xonar has hardware Dolby Headphone acceleration, which provides positional audio to normal headphones. But I don't use that myself, I have an analog 5.1 channel headset (Roccat Kave 5.1), so I can let the normal surround sound do it's thing, rather than relying on hardware post-processing.

I'm guessing I hear the full brunt of the audio Sins can through at me, but I can't really see a way to test it.

Yeah, I wish there were a sound.log for this game.

If you're up for a little experiment I'd be interested to hear the results.

I am assuming you've already changed the line in the rebellion.user.setting from

SoundUseHardware FALSE

to:

SoundUseHardware TRUE

If so, please right click on your Sins of a Solar Rebellion.exe and configure it to run in compatibility mode for WindowsXP SP2.

Play the game and let me know if you notice any audio differences.

The effect is noticable, music gets a little more muffled (although not by much) and the sound-effect quality deteriorates quite a lot, distortion is a lot worse with "SoundUseHardware TRUE" and compatibility mode set to XP SP2/3. Individual sounds are audible, but there  are small clicks and crackles all over the place (especially noticeable on rapid fire weaponry), which makes sense as the Xonar does most of it's audio processing in software rather than hardware.

Sound Quality with "SoundUseHardware FALSE" and everything else set up as normal is quite a bit better with sharper music and each individual sound effect clearly distinguishable, as well as directional audio cues when zoomed in to a battle scene, these directional cues were much harder to hear with "SoundUseHardware TRUE" active.

So to conclude, this card doesn't provide true hardware accelerated audio, turning it on makes the experience worse.

For EAX does it do hardware post-processing, and all the hardware Dolby/DTS encoding obviously.

This is a card pretty much designed to work within the Windows Vista/7 audio paradigm though, so it makes sense that treating it like a card designed for hardware audio under Windows XP doesn't do it any favours.