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Guessing it's the cleaning of the filter. Personally I find the V60/Clever Drippers a lot less faff due to just chucking the paper filters out (obviously not applicable if you're going the cloth/metal route). But even the Technivorm/Moccamaster brewers will have the same amount of cleaning. Unless it's the pouring that's a faff. Personally I've never found an issue with that, but then again I'm happy to use a siphon for a daily brew.
Chemex might be a decent middle ground as they're big enough that you can get away with just putting all the water in at once as opposed to the more steady/intermittent pours that are normally required by the V60.
Though having written all of this, assuming the Clever dripper is big enough, that seems like your best bet.
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I think it's more of the issue with the small grit that gets through the mesh. Clean-up is otherwise easy, I just prefer no fines in my cup.
Clever Dripper may be an answer but I just had a look at the Hoffmann method for the Clever Dripper and it looks like more faff.
I am just being lazy and want that second cup on demand, as opposed to setting up for another brew.
I'm not sure I understand this. What's faffy about a French press? Do you mean you have a small one that can only do one coffee at a time?
We have a 1L insulated french press that can do three coffees in one go. Keeps it hot for an hour or so without overbrewing too. Not that it ever lasts that long.