yes, LP is an expensive heat source, and since it costs more, that is even a better reason to go tankless - LP tankless units only cost an extra $30 for the correct orifice? (are you using propane for water now? or electric, or fuel oil?)
they work best if you are "away" alot. I go to the gym in the morning - shower there. we are away one weekend a month (at least) - nobody is home during the day 8-6, and we are asleep 10-6 - I switched from electric to NG - and i watched the electric bill plummet, and the NG bill barely budge.
(i'm thinking $60/month to go electric to tankless NG 5 years ago like $80->$20) we run the dishwasher every 3rd day (it has a heater to bring the water to needed level), laundry every 3 days - mostly in cold tho -
i could probably go and pull out my old bills and do a more analytical approach, but i was very happy with the results.
there are two gotchas
1. is that suddenly, you could find yourself taking a 20+ minute shower, just because you can!
2. if your input water is cold, you may not be able to get enough gain to be happy with the "hotness" of the water, especially if you are at high altitude.
I think they post cost estimates - take their view vs your current and see how it does.
please post any research findings you come across - i'm sure many people are very interested in this subject.