As much as it seems a waste to dump cold water, you'll never recoupe the cost, it will actually cost you more. First you have to pay for it, and second your water heater will run more. Water is so cheap the volume of water you dump is tiny.
Electric's OK if your main heater is electric, if you main heater is gas, better to dump the water.
Best bet for result you'd like would be to replumb using pex tube so you cut the volume of water in the pipe by 2/3s.
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