Question on the feasibility of res upgrade...

Hey all.

I'm currently running a single plant grow in a GH WaterFarm 4210 (the single bucket stand alone model). Everything is going pretty well so far. However, in about a month I will be leaving town for about 4 days and I need a way to keep the res full. By then I estimate she'll be drinking about a gallon per day. GH makes an 8 pack version of the waterfarm that I'm sure most of you have seen. I was considering hooking up a GH Controller unit to feed her while I'm gone, but the controller section of the unit is significantly bigger than the res on my WaterFarm, and since it is gravity fed I'm not sure if this will work or if it will just overfill my res. Advice from anyone who has attempted this, or who has a better grasp of basic physics than I would be greatly appreciated!
First pic is the controller unit (8 gallon controller under a 20 gallon res.
Second pic is how the 8 pack is normally set up.
Third pic is my WaterFarm (4 gallon bucket, 2 gallons of that is res space)

Biggity bump...

Put a float valve in the small rez, run a 1/4 inch line to a larger elevated rez. Simple, gravity fed, cheap.

Good call. I was kind of hoping GH unit would be a simple fix, but your suggestion wins on price and simplicity. I'll just have to figure out a way to mount the float valve.