I found a 'water mixing calculator' online, and it appears if I set my tank at 100 degrees fahrenheit and my winter cold water is at 37 degrees, the amount needed of each to reach 68 degrees is pretty much 50/50.

So, if the washer sips water at a rate of 700ml a minute for an hour, it'll use 21 litres of hot water, or 5.5 gallons. If the tank is set even higher the hot water volume would be even less, so a 10 gallon tank would be plenty big enough. If I noticed the temperature dropping as the tank was getting drained of hot water, I could run another hot water faucet to 'kick start' the tankless heater to re-fill the tank with hot water again.

Interesting stuff