400 watts is a lot to pull from your vehicle cigarette lighter. If you do connect enough devices, you could blow a fuse depending on your vehicle. I do like the vehicle power inverters for their convenience for some devices but really not necessary in this case. In any event, just be careful how much power you pull through it.
When considering switching to the Tandem t:slim X2, I was initially of the opinion of @rgcainmd and thinking replaceable batteries would be better for a pump. That is what we were used to - the standard AA lithium battery. Easy to get anyway and always a good supply kept on hand.
However we found our reality (after switching onto the Tandem t:slim X2) was more of what @ccc mentions when they say it was found to actually be less of a hassle.
Here is a nice article from the Tandem Diabetes website in regards to charging preferences from a (likely non-scientific) survey done on their user base:
For portable charging, we use @Sam19 suggested approach of the portable batteries. We carry portable batteries. We also use a dual USB charger in our vehicle that plugs into the cigarette lighter. These are all standard outputs and are not a problem at all with the t:slim as well as being able to keep the Dexcom receiver charged, the iPhone, the Android, all the gear.
My choices for charging all these devices (on-the-go, vehicle, home):
https://www.amazon.com/gp/product/B00EETOTWS/