I have a large shower with body sprays and was told I would need two regular gas heaters or a large one so paid the extra for a condensing gas water heater, 130k BTU (standard is about 40 - 50 k BTU I think). It can be vented with PVC pipe as it extracts more heat from the flue gas making it cooler (and water will condense out, hence the "condensing" type). It cost about $2700 about 8 years ago.
I also installed a GFX heat recovery drain pipe device. It is just a brass section of drain pipe with coils around it that goes in a vertical drain stack. As the shower drain water goes through it the heat is transferred to the water going into the heater. They claim about 60% heat recovery. I just know it works very well and no moving parts. I think it was about $350 but that was about the same time and before copper prices shot up.
I think trying to change the temp of the tank at different times of day is going to give little, if any, savings. You could probably look at other things that have a faster payback.
We heat a 4000 sq. ft. house in the midwest and heat the garage a bit (50 degrees) as well and have budget billing of $45/month for gas - space heating, stove, grill, and hot water.
The sensing of shower with flow meters and such is interesting. I looked at taping into the water softener flow meter but it was total water flow (hot and cold) so I took a simpler approach. I just put a push button by the shower and hit it as I am getting ready. It triggers a circulation pump to run for 30 seconds and fill the pipes with hot water. What I haven't done yet is interlock the hydronic floor heat that also uses the same heater (through a heat exchanger so the floor loops are isolated). The floor heat will pull the tank temp down so I want to disable floor heat for about 45 minutes when the button is pushed. Being off that long will never be noticed for the floor heat.