I have now built 4 container bogs using masonry tubs and a whiskey barrel liner. Each time the "plumbing" is different because I went to Lowes or Home Depot and put together pieces that worked based on what they had. I laid it out in my cart to be sure I had all of the parts. Glueing together PVC is very easy with the glue (that is likely highly toxic and should be used outdoors).
Basically decide what size, I have used 1 and 1 1/2 inches, then put together the puzzle of elbows and caps so it works. PVC cutters make cutting super easy. And buy a long piece of pipe to be the long pieces and clean outs.
I think a waterfall back to your pond is your best bet. It doesn't even have to be higher than the pond level, since the water flowing through the bog will rise up and join the rest of the pond water. The wall between the pond and bog can be below the water level. It for sure should be lower than the other 3 walls of your bog. I do not think a pond spitter with have enough volume to do what you need.
On my last bog build, I made the container within the pond so if it overflows the water is still in the pond. It is somewhere I do not check every day so I was more worried about failure. This could be an option for you. It could be put in almost underwater so it is less visible. You could use any shape container. I liked that the whiskey barrel liner had a built in weir.
The plants will grow in and cover it. This could work for you and does not require emptying the pond or messing with the liner. I put it on concrete blocks. you could put some underlayment so the bricks won't damage your liner. I will attach pics. I wanted mine raised high since this is the aeration on this pond. There used to be a waterfall that failed. And I needed a quick solution of bog plus waterfall.
It is hard to see from the pic, but the water comes out the weir and due to the tilt of the container, it is also overflowing in the back. I was glad it was doing this to keep water circulating at that back corner of the pond, or I could have leveled it to only come out the weir.
My first container bog, I cut through to have the pipe enter in a more hidden way. But the plants filled in so much I am confident the cleanouts and water inflow line will be camouflaged when this takes off. This container is 26 inch diameter and I forget the height.
**The bog failures I have had are #1 pump becomes clogged and slows the flow. So I have to turn the pump off and spray with water to clean it. #2 is roots grow and push up the rocks and create dams that make my bog overflow not into the pond lowering the pond water level. I have fixed this by taking out gravel and digging down channels to help the water flow and stay in the bog and flow out where I want it to. This is why I wanted my newest bog completely within my pond.