I tried to find a valve similiar to what you are describing when I built my bucket waterer, but they are not sold in my area. The closest thing is a float valve for a stock tank and it is more expensive. I like the idea of a side valve going straight to the poly line without the adapters, and I found a similar valve that I am going to try for $8. The toilet valve coming out the bottom doesn't cause any problems, but the advantage of going straight to the poly line is worth looking into. The toilet valve does have one advantage as the fluidmaster can adjust to vary the depth of the water. I searched Home Depot's website as well as Lowes with no luck in finding the valves, maybe because my home store doesn't have them. Would you post or send me a link PreppingMom?
I have a cross bar out of 1 1/2" pipe and a top perch out of 2". My chickens have no problems getting to the nest boxes, even the Bantams can get up easily. At night the chockens roost on the perches and in the nest bpxes.
I drag my chicken tractor around myself, and have moved it pretty far before. As long as you are going across level ground its not bad at all. My wife can drag it too, so it can't be too bad. I see no reason why it couldn't be moved with an ATV or a tractor, but I wouldn't bother with using one.
I have 16 chickens in my coop currently and the bucket has enough water for atleast two days in late summer weather as I didn't have the water on at one time. The good thing with the bucket waterer is there is no waste or evaporation. I am going to run some tubing to the outside of my coop from the bucket waterer and connect it to the bottom of a length of 3" PVC in order to fill the bucket waterer manually without having to climb into the coop and take the lid off just for situations in the future where I don't want to run the line, or winter filling.