Slight hesitation on my part to say anything here as I have a MS 400 not a 350 and they are different boats. But on my boat it would be an easier wire run from the cockpit to the main DC panel than it would be to go directly to the battery. Assuming the voltage drop would not be too much (you need to measure from the battery to the panel to the outlet AND back) a breaker on the panel would be a much better solution than an in line fuse.
I also don't like adding any more wires than absolutely necessary directly to the battery. You probably have some sort of positive and negative buss bars down there that you could pull from.
Inverters draw a lot of power when the load on them spikes, even at 350 watts. They are bad about tripping breakers, in my humble experience anyway.
Just my .02 cents. C-Electric and others on this thread know WAY more about this than I do.
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