I'd love to see some build specks but if you have a super clean keg and lots of line, you can carbonate by shaking and rolling it on the floor for about 2 hrs or more at very high pressure but really cold as well.
Best option would be to just wait or get a
carbonation stone to do it for you.
The build was fairly simple. My kitchen and garage share a common wall. The kitchen sink is on one side and the kegerator sits in the garage on the other side of the wall. I have a 6 stage Reverse Osmosis/ De-Ionising filter set up (I bought it from US off eBay and installed it myself. A third of the price of one from a local water filter shop)
Water runs from the mains tap through three carbon/particulate filters, then through a reverse osmosis filter. It then passes into an 8 gallon pressure tank. The line comes off the tank, passes through a 5th polishing filter. It then splits three ways. One goes to the filter tap for drinking water, one goes through a hole in the wall, into the back of the kegerator and connects to the carb keg. The third line passes through a final De-Ionizing filter and ends in a hose with a ball-tap. I use this water for my saltwater aquarium (DI water is not suitable to drink but is important for reef-keeping).
The fizzy water comes out of the carb keg, back through the rear of the kegerator, through the hole in the wall and connects to a 2nd filter tap on the sink.
I have about a metre of hose with carb water in it between the fridge and the tap. I estimate this will be only about a shot glass of warm water. I can run the tap for a second or two before filling the glass to ensure cold water or just not worry.
I actually contemplated putting the RO pressure tank in the fridge as well to have chilled still water from the other tap, but it was more trouble than it was worth and frankly it took up too much space in the fridge that should be used for beer. I can now have two beer kegs on tap in the garage and endless fizzy water on the kitchen.
I tried to convince the missus to let me install a couple of beer taps on the kitchen counter and run the beer through the wall as well. Needless to say it was not met with enthusiasm.
Eventually I’ll upgrade to a Kegerator X for four kegs and look at putting the RO tank in there for cold filtered water but I need to get a few years out of the current setup before wasting money on a fridge upgrade.