When i hear you say 'shanty boat' i'm imagining a barge or maybe a scow hull, is that right? Sheltered waters, not much moving around? Towed or under power, but not sailing? I guess my main concern would be that what the boat needs to function as a boat comes first, and if a stove can fit within those parameters then carry on. It seems like it would be hard to get the weight very low in the hull as the heater is going to need a certain amount of vertical height to function and if you want it as a bench it's already above the sole.
I'd want to consider how angle of heel changes the geometry, especially if i was sailing, but even if i was just going to be rolling a bit in the slop. It might change the relative heights of inlets and outlets in the bell as the boat rolls or pitches which could do weird things to the draft. (especially if it's not symmetrical along the midline)
I'd want to build it so it held together and was absolutely secured to the hull, a few hundred pounds of stove coming adrift in a seaway could be real interesting.
If you're burning beach wood you might create pcb's although the hot fire would help. At any rate, the salt fire can also wreak havoc on metal bits pretty fast so i'd try to build it so i could replace ducting without too much hassle.
If it's down low and in the bilge a bit, watch the galvanic corrosion and careful with using dissimilar metals in contact with each other, or immersed, or connected to your hull depending on what it's made of.
If you're tied to a dock or have a stern tie or stern hook or have strong tides, then the wind will come from everywhere...if you're going to be lying to a bow anchor(s) the wind is going to hit the boat at the same angle most of the time and you,might be able to design your set up to get a draft benefit from that.
Will you have gas and or (especially) propane on board? Will you need a bilge blower and gas detectors? Don't make any
wells or pockets that can trap propane settling into the bilge from a leak, you've got an ignition source right there. That might be my biggest worry.
Can you afford the amount of space this thing will take? It's going to have way way more volume than an equivalent lead ballast, and volume = more construction time and more money or a lot less living space...
I'm probably the wrong guy to listen to as I'm pretty trad. when it comes to boats...i'd probably be casting a lead ballast keel and putting in a nice
cast iron woodburner. But it's an interesting idea.