There are safeguards that you could easily implement to overcome most of these. First, get a good idea of the amount of evaporation. Second, get a reasonably sized container, such as 5 gallons or so. You can set the pace initially higher than necessary, since the pressure will reduce with time. It can and does even out and can work well if done properly. I did it many times.Usually most LFS provide a service to come care for your tank. If you trust them in your home that is probably the way to go. It's worth the money for you to not worry the entire trip. Trust me.
I wouldn't recommend the 'drip' system. One of two things will happen over that amount of time.
1) You won't set it to drip fast enough, the water will evaporate within a week to the point where your pump is sucking air. Your pump burns out and all your fish die before you get back.
2) You set it to high and you come home to whatever amount of liquid you used as a reservoir all over your floor.
Their is basically no chance of getting it 'just right' over a 3 week period. If you want to try, you need to start it now and adjust it for as long as possible as accurately as possible before you go.
One thing I did overlook, however, was the time frame. I missed the 3 weeks part--I only saw "week," so I assumed that was the maximum amount of time. All this being said, the safest option at this point (ATO may be risky, especially since you won't be there to monitor initial operation) is to have someone watch the tank.