Replacing it with another gas HW heater would have far lower operating expense than an electric HW heater in your area (unless you went with a heat-pump hybrid type at much bigger upfront expense, in which case the operating costs might be comparable.)
Turning off an electric HW heater for 12 hours/day with a timer has almost zero impact on the amount of power used. Electric tanks have very good insulation and very low standby loss. To get a significant reduction in standby loss and savings would require a big drop in the water temp during the "off" period, but an electric tank set to ~125F would typically lose less than 1/4 degree per hour, so you'd still be over 120F at the end of your 12 hour period. The vast majority of the power use is for raising the 55-65F incoming water up to the 120F-140F setpoint temp- the difference in standby power use between water with less than a 5F average difference is truly in the statistical noise- low single-digit percentage savings on the overall power use at best. Only if you can get a rate reduction on your electricity bill for heating water only during off-peak hours would a time-of-day approach make any economic sense.
Whatever heater you install, you get pretty good payback on 5/8" wall closed cell pipe insulation on all the near-tank plumbing (including the first 6-10' of the cold-feed closest to the heater and the temperature & pressure overflow valve & outflow plumbing), as well as any hot water distribution plumbing that is accessible. For a primer on how to do it, see: http://www.leaningpinesoftware.com/h...er_pipes.shtml