To get a useful temperature rise with an electric tankless requires a HUGE power input. Probably work fine for a shower, but not so much for filling a huge tub in a timely manner.
80-gallons of water weighs about 665#. Say your water coming in is 50-degrees and you want the tub at 105 or so...that's a 55-degree rise times 665# = 36,575 BTU and your valve can flow 8g/min (say you are using a 3/4" valve to fill the tub faster than a 1/2" one). That's 1/6th of and hour, so since burners are rated at BTU/hr, multiply that 36575 * 6 = 219,450 BTU/hr. Now, you'll probably want the hot coming in a bit higher and mix some cold with it, but that's already more energy than a typical gas-fired tankless can provide, and if your wintertime cold water is colder than that, the energy needed just goes up proportionally. Where I live, my wintertime incoming water has hit just above freezing with a measured 33-degrees, adding a significant increase in energy required. That 219,450 BTU/hr = 64,314W. IOW, forgetaboutit doing it with electric. You could use one as an inline heater to boost the temperature when filling the tub from the tank, if you wanted.
To cut down on the time for hot to arrive on the other side of the house, consider a hot water recirculation system. That will allow you to get the full capacity of the tank to feed your tub since you won't be throwing away a few gallons while you purge the lines of cold and warm up the pipes. If you can install a dedicated return line, all the better, but the retrofit systems that utilize the cold line also work. Mine is one of those. I find that if I flush the toilet before trying to use the hot, my cold line is purged of the warm water. Keep in mind that the systems turn off when the water gets warm, not full hot, so hot is nearby, but that also means your cold line isn't heated very much. Depending on the system you buy, that cut off point could be anywhere from say 85-105 degrees, and some of them are user adjustable. I find that when mine shuts off, hot is a few seconds away from my tub which is closer than the sensing location (under my sink). A recirculation system could be setup to be on demand, on a timer, or manually activated when needed. The one I'm currently using is made by Lang. The old one I had lasted nearly 20-years, and the company went out of business, so the part I needed (proprietary) was not available, otherwise, I'd still be using that one - the pump was fine.
