Well, assuming no losses, heating 800 litres of water from 12°C to 45°C in 28800 seconds (8 hours), would require a 3.5kW heater and in that time burn about 31kWh of electricity. ( Heat value of 31kWh approx 107000btu )
Engineering Toolbox gives the Net heating value of Propane as 19834 btu/lb, so about 2.5kg of gas would be burned heating 800 litres (5.4lbs of gas).
Electrical heating is more efficient in that the element can be buried inside the water and the whole lot insulated. Not difficult to waste less than 10% of the heat input.
Gas is cheaper than electricity but it's much harder keep the heat in. The firebox part of the tank can't be lagged, and whatever is done in the way of lagging a fair about of heat disappears up the chimney. A full-size steam locomotive boiler won't be more than 80% efficient, and 60% or less is more likely. Big boilers are more efficient than small ones because they have a better ratio between volume and surface area. Low-temperature heaters are less wasteful than high because heat loss is proportional to temperature difference. Water tube boilers are more efficient than fire tube types, and most Marine boilers leave steam locos in the dust! (Not least because ships can accommodate heat recovery systems and thick lagging.)
There's a relationship between the size, number and length of fire tubes needed. Too few and too many both waste heat. I can't find the book covering this aspect of boiler design, it's to do with balancing the surface area of the tubes with hot gas flow so that the maximum heat is transferred: a single big tube is fast and wasteful, many small tubes are too slow and choke the fire. Perhaps someone else knows – it may not matter much in this application?
I don't know how efficient a home-made gas heated 800 litre boiler at 45°C could be. I guess a big fire tube boiler would be good rather than bad, so maybe assume 70% efficiency and expect to burn about 3.2kg of Propane over 8 hours.
Assumes all 800 litres of hot water are used and the tank is completely refilled with cold water every 8 hours. Consuming less than 800 litres would save energy, as would using waste chimney heat to pre-warm a feed water tank. (If there's space!)
I don't know anything about PSB burners either, but to give an idea of size small cooker gas-rings are about 1kW and large rings 3 to 4kW. Nothing terrifying needed! All seems do-able to me, just make sure there's plenty of air and the tubes flow well enough to stop an over-lean flame producing Carbon Monoxide. (Definitely buy a CO detector!)
Dave
Edited By SillyOldDuffer on 19/06/2020 14:28:48