Yeah my buddies and I have had a real problem with the PS4 and capturing party chat too x/ I've figured out a workaround for the Elgato HD60, but I'm not sure if it'll work for the Live Gamer Portable. Anyways for the Elgato the fix is really simple and all you need is a spare Microphone (I used a Blue Snowball) and a free computer with a spare USB port (you can probably just use the one you're capturing the footage with).
Unplug your headset mic from the PS4 and plug your spare microphone into where the headset's USB used to be. Plug your headset into your computer's USB port to keep it powered and that's it! However make sure that you're recording your own audio with your regular mic and audio recording software (like Audacity) as doing this only records everyone else's chat audio.
For some reason chat audio and gameplay audio can't be simultaneously recorded together on the PS4 like it was for the PS3 so you kind of have to "trick" it with your spare microphone. Btw I use a wired headset tho so if you use a wireless one I'm not sure if this will still work. Anyways I hoped that helped man, not the most straightforward but it's the only one way I know
I'll look around a bit to see if I can find some solutions for the LGP! - Brandon
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