Not actually adding a lot here, but the sloshing sound isn't just water rushing through the heater core, it's air as well. Water moving is quite quiet, its the air mix that produces the noises (most of it, not all). I would consider trying to get any air out of your core and lines if you can, as that'll cause issues with the pump and/or overheating (worst case scenario). My car has been doing that for a while now, just haven't gotten off my tush to fix it, so it's not bad, but not good either.
__________________
|