I'm not sure but I don't think editing the save files will fix this issue. Are you sure that all your available saves are from the point where you were already missing the third pipe?
Anyway, the save files can be found here:
Windows Vista, 7 & 8: "My Documents\Amnesia\Main\"
Linux: ".frictionalgames/Amnesia/Main/"
Mac: "Library/Application Support/Frictional Games/Amnesia/Main/"
I was going to suggest giving you a save file from the start of the Control Room, but I've just realised that on my main profile I only have saves starting on the Nave area (which comes later in the game); on my secondary profile I do have a save file from the beginning of the Control Room, but the problem is that I was speedrunning so I didn't pick up any items at all: at that point in the game I've got zero notes, tinderboxes and laudanum flasks, and I only have a few drops of oil in the lantern. If this is not a problem for you, I can attach the save file here.
Or maybe someone else can provide you a save file with all the notes and some tinderboxes/laudanum/oil, if that's important to you.
I had a backup folder with a lot of save files from previous playthroughs, but I deleted it a couple of weeks ago to free hard drive space. Bad timing