The last thermostat I replaced on a water heater just had two screws and the electrical connectors and took about 10 minutes to change out. They are typically located under removable covers on the side of the water heater.
Most dual element hater heaters switch between the two elements. The top one heats first then the bottom one second. The top element is usually set up with a DPDT contact system so that when it reaches its set point then it switches off and sends power to the bottom one. For limited use applications just dont use one.
Being mainly for weekend use just wire up a simple on /off switch to manually turn it off or put a automatic timer on it. They are cheap to buy now as well.
As far as heating water goes, one pound of water raised one degree F takes one BTU. From that you can determine how much energy a specific mass or flow rate of water will require to raise its temperature by a specific amount.
I know several people who have had the on demand water heaters before and everyone of them said they saw no real energy savings but they did take a lot of almost warm showers until they switched back to the old tank style water heaters.
The problem is as you may now be aware of heating any reasonable volume of water from a low temp on demand takes a considerable amount of electrical power.
A 100 F temp change for a basic 1.5 GPM flow for a shower takes around 1.5 x 8.33 x 100 = 1250 BTU per minute or 1250/3.414 = 366 Watt hours per minute which is 22 KWH of power or 22,000/ 240 = 92 amps at 240 volts!
I hope this gives you a better idea of the actual energy levels in electrical terms that simply heating some water takes and why the high priced on demand systems dont justify their costs in many applications.
I suspect the price paid for the unit plus the electrical and plumbing costs where several thousand dollars if contractors did the work. For that cost your old tank heater probably could have sat unused at full temp for the next decade and cost a lot less!