Numbers seem to be pretty close:
1gpm x 8.5lbs x 60 min/hr = 510 lbs water / hr
510lbs water x 45F delta T = 22,950 btu
You say 3.15lbs x 8000btu = 25,200 btu input
Finally 22,950 btu out / 25,200 btu in =~ 91.1% efficient "apparently"
I throw the "apparently" in there because several things can affect this calculation. What types of actual temps are we talking? What is the initial temp of the water? What is the final temp? What is the ambient temp while the run is happening? We are talking 1gpm of 'new' water for the whole period...'cause circulating 10 gallons of water at 1gpm changes things substantially! Is there electrical input for pumps, augers, conveyers, blowers, etc.
For instance, I could draw a 55 gallon drum of well water at 60F, leave it to sit in the afternoon sun with a small candle beside it and come back to find it's 105F in the afternoon. I find the amount of candle burned is a few hundred btu and the water has increased by thousands of btu. So did I get 1000% efficiency from that candle? Well, no, not really - heat snuck into the system from sources which weren't considered in the original equation... the sun! A super efficient water heater in the summer is not hard...on a -10F winter day...considerably more challenging.
Likewise if this is a circulating system...you can only consider the weight of water in circulation, not the actual gallons of flow. Say I have a 100 gallon tank and a 100GPM pump and the heat goes up by some amount in an hour...I can only consider the 100 gallons or 850 pounds, not 100gpm x 8.5lbs per gallon x 60 minutes = 51,000 lbs. Further, relatively large pumps on relatively small volumes can add a notable amount of heat. I have a hot tub heated only by the 7hp jet pump...1hp is about 2550 btu - so if this heat is fully captured, it can add to the total considerably.
On the 'plus' side, technically you should consider the heating of any storage tank, piping, water pumps, hoses, etc. Those all have thermal mass and are being warmed by the heater as well.
Modern 95% efficient boilers can be had...so efficiency of this level is not out of the question, but they need a clean burn and actually condense the water out of the flue gas to recover that extra bit of steam energy. Of course, heat pump water heaters can approach a 'coefficient of performance' (COP) of 2.5 or better...which is 2.5 btu out for 1 in, or an apparent efficiency of 250%.
One concern - you mention a lot of charcoal being produced in this system? Charcoal is carbon and carbon is energy, so if the charcoal is piling up in huge amounts a lot of energy is going with it. You also show a pipe with steam coming out? Heated water or wood exhaust? If this is wood exhaust, that steam itself has recoverable energy when it condenses, so again piping away more energy.