Hope all is well with the offspring in the A+E!
I'm pretty certain that John had it spot on with his diagram. The pipe with the red valve on is the sump feed/weir height level adjuster. The tall pipe is just an overflow pipe in case something blocks the flow through the sump feed, causing the weir to fill up.
It won't be that hard to silence the tank. It all depends on the type of bulkhead that connects to the downpipe, as to what parts you are going to require. What you are aiming for is something resembling the picture in my earlier post, to come up from the bulkhead, with the tee/90 degree fitting maybe 1-2" below the height of the weir comb. That way you won't get a cascading sound from the water flowing into the weir.
If its a solvent weld fitting, then you'll need a length of the appropriate diameter pipe, probably 32mm but might be 28mm or 40mm (just measure the diameter of the red valve tube). You'll also need a tee section, a 90 degree elbow, and an end cap. I'd get a couple of end caps, because you have to drill a hole in it. If you manage to screw it up, then at least you'll have a spare lol. Also, get a couple of rolls of PTFE tape (white stuff used for plumbing fittings) and a tin of solvent weld (Black Swan is good).
Assembly is pretty straight forward. Personally, I would not solvent weld the pipe into the bulkhead. If at some point it needed cleaning, or something got stuck in it, you'll be up the proverbial creek without a paddle, as you'll be unable to remove it. For that, I would wrap the end with PTFE tap, so that it forms a nice snug push-fit. You can solvent weld the tee-piece onto the durso pipe and the elbow to the tee. The end cap you might be better off with just using PTFE for a nice tight fit. That way you can remove it if need be and insert a rod down to remove any blockage.
There is a chance that the bulkhead will be threaded. If so, just do as above, but solvent weld a threaded adapter to the bottom end of the durso. This may require a reducer too (
see link for parts list). Again, if a blockage should ever occur, you can unscrew the standpipe from the bulkhead to access it. Just make sure that you can rotate the pipe with the tee/elbow/cap connected or PTFE that part together so that you can remove the inlet assembly (tee/elbow/cap) and then just rotate the pipe to unscrew. Another option would be instead of using the PTFE tape, to use a compression coupling on the pipe below the assembly instead, which you can unscrew to remove it, then twist the pipe to unscrew that. You have a few options available. Basically you want will silence the tank but also enable easy access for servicing if need be.
The key element in all this is the hole which you will have to drill into the end cap. I'd personally start at 3mm and work your way up in 1mm incriments. The idea is that as the water enters the tee piece and falls down the pipe, it will draw air in through the end cap hole. If there is insufficent air, the durso will go into full syphon and basically auto flush like a toilet until the weir drains below the level of the tee piece, syphon is broken and the weir fills up again. If this happens, remove the cap, increase the drill hole size and repeat the process. You don't have to worry about the weir overflowing as you have the fail safe pipe, that John pictured in his diagram (green one). We want to create the durso where the yellow pipe is, although make it about an inch or two below the weir comb height. In the unlikely event that your durso becomes blocked, you will be alerted to this fact by the noise you currently have from the tank, as the water will be flowing down the unsilenced green pipe
Once the durso is functioning properly it will be virtually silent, just make sure that the valve in the sump cabinet is at full open position, as the durso will make it redundant. Its still worth keeping in there though, as it enables you isolate the weir section if need be. The only other issue you might have will be gulping/burping coming from the sump. This you can resolve by shortening the pipe with the red valve to about an inch above the water surface in the sump, then fitting a tee section to it, which should make it about level with the water surface. As my sump is getting a lot of fish poop collecting in it, I'm going to be fitting a 100 or 200 micron filter sock to my sump feed. Hopefully this will collect a decent amount of poop, which I'll empty once or twice a week, depending. If the 100 micron doesn't enable enough water to flow through it, then I'll go to the 200 and see how I get on.
So measure the pipework, shut the pump off and check the bulkhead type, then get down to plumb centre!