I didn't read whole thread...
You can solve the cable problem by getting an extension from eBay. While you're there, get an adapter cable that converts the male cigarette plug on your inverter into battery clips, just in case you blow the cigarette outlet's fuse when you're "out there." Both items should cost you about $15 from eBay.
That product in the Amazon link looks good enough. Your limitation here is the weak cable between the battery and the cigarette outlet. So, you should make sure to keep your ego in check when buying an inverter for your purposes.
I have an inverter that's more powerful than necessary, and thus bigger than necessary. If I were to buy right now, I'd get something like the inverter in the Amazon link.
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If you're reading this, it's too late.