Ahhh I know this situation all to well. Sir I hate to say it but if the coolant level is dropping and your seeing gunky stuff well that sounds like your heater core. There not cheap and there not fun. The thermostat shouldnt have much to do with that and plus its pretty dang hard to install one backwards. But otherwise yes the spring side always faces the engine in my experiences. Now heres the thing I would ask someone on here who knows about your vehicle a bit more on the subject of your heater core, cause the only ones i have had to mess with have been on a pontiac.
So I hope this helps a little bit-Nick