pianotuna> Well, I'm going to stick with what I have experience with and that's nothing on 12V appliance capabilities other than the fans in my rig. I'm lazy, I like electricity, and I'll admit it.
Altho, if you do decide to part with the money for one, I'd be interested to know if they actually do the job well. You have an interesting concept for using them that might be worth trying.
However, I do have a background in electronics. Notwithstanding the heat issue mentioned by GW, the DC plugs in your rig are generally on separate fuses. Most are 5-10 amps. The cigarette lighter is usually 15 -20 and will handle a high current draw 12v appliance. The ones for things like a tv, fan, or the like may not. If you use one of the after market multi-plug adapters to plug more than one appliance into a single DC socket, you certainly increase the odds of blowing a fuse. So either way, please be aware of the amp ratings of the fuses. The amp rating of the appliance will be listed either on the label or in the manual that comes with it. 12v electronic items that are UL approved also come with a fuse built into the DC plug. They usually have an amp rating less than what your rig's socket fuses will be. That's a convenient safeguard that blows the appliance plug fuse before you blow the rig's socket fuse. It's easier to change that than it is to stand on your head, holding a flashlight up under the dashboard, trying to change a blown fuse. That is IF you can find it under the dash
Another thing to consider is the length of the cord that you need to run to plug an appliance into a distant socket. If you string out a bunch of wiring, you will increase the resistance which in turn increases the current draw and can overload the circuit. Result = blow fuse.
Since you have an inverter, have you tried using it to power a regular slow cooker while moving? My rig also has an inverter and we use it way more than we use the generator. I use it to power the fridge instead of using propane, run the laptop, and cook a quick microwave meal at a rest stop. The batteries that it draws power from are being recharged when the engine is running so battery drain is not an issue.
If you do use the inverter for dry camping needs, I would respectfully suggest that you buy a plug in volt meter to monitor it's output. They are about $15 and plug into a regular AC socket anywhere in the rig. You can monitor the voltage that is being used. If the needle drops out of the green arc, then you are overloading your inverter by using too many appliances at once. It's also good to monitor voltage when you are plugged into shore power. Low voltage is very bad for electrical appliances.
I have an image of your meal being "hurled" all over the floor. Probably not funny tho, huh?