Combining solar hot water, on-demand propane back up, and a good thermostat will get you hot water when you want it. Between solar pre-heating, insulating the tank, and having a little propane to boost it to the desired temp it should work just fine and use minimal fuel.
Dave
Principal - Terra Phoenix Design
http://TerraPhoenixDesign.com
If your water does get cold, remember that it's actually better for your skin to shower at night. Gives your body a chance to replenish the oils you wash away with soap & water.
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40 things, worth over $600, all for $35 - the permaculture adventure bundle