Even if it worked it wouldn't matter as long as Egyptology can see only ramps and won't do any testing to falsify them. Everyone can just forget about anything other than ramps, tombs, bumpkins, and changelessness because this is all settled science. If you could prove that there are ruins of a canal almost exactly where you depict it IT WOULDN'T MATTER because it would be interpreted as a means to slake the thirst of an army of stone draggers. I've searched everywhere for canals starting within days of figuring this out back in '06 and could find nothing. This was one of the first places I looked. Of course I could have missed canals ANYWHERE because even their ruins could have been hauled off and little scar left on the earth. This is your big problem; no evidence and Egyptology doesn't care anyway and Peers determine reality with or without doing the testing. This is the world and today's emerging dark ages.
Then there is you logical failure as well. In order to handle the volume of water during rain events the canal below the Tomb of the Birds to the west of G1 would have to be 10' wide and building this on the side of a cliff would leave an enormous scar and ample evidence. There was lots of runoff in rains but it was very brief carving out wadis but leaving little moisture behind. They got a few inches a year but very little during the summer which was pyramid building season that started on the five epagomenal days just before the first day of summer. Any significant rain event might be able to fill the catchment area around the pyramid but this would only be 50 acre feet at most probably. This is a mere 55,000 tons of water. Operating in funiculars this would only raise about 40,000 tons to the base of the pyramid from the valley port that Egyptologists laughingly call the "Valley Temple". Even if they got a couple such rains in the summer it would probably be insufficient and we are still left with needing any kind of means at all for lifting the stones into the pile that looks like G1.
Certainly you have a very valid point that they could harness rain to supplement any other source of water they "mustta" had. 50,000 tons of water at 225' is nothing to sneeze at and it's not too hard to imagine they could acquire this without too complex a system that left no more evidence than the ramps we know they had to have used. You know those ramps we know existed without ever looking for them because it's the only technology they had. At least they did actually have an "Overseer of Canals" rather than the imaginary jobs we believe in today.
I hope you do find the canals. I interpret it to refer to the NE and NNE Trench but the PT do mention "knsti-canals" a couple times as being a part of the "Winding Watercourse". "Knsti" means "desert's edge" so it's entirely possible that this is exactly the canal you seek. Of course, it's possible this has been retranslated to mean "ramp" now that Egyptologists have had a century and a half to study this in terms of the "book of the dead". The old translators found a lot of water in the Pyramid Texts and even referred to columns of cool effervescent water that came from caves. In the old days this was all taken metaphorically but now it seems to get closer and closer to fitting all the assumptions. The old translators knew they didn't understand the writing but today I often don't even understand the translation and have no clue what they mean.
I would suggest you expand your search. Anywhere within a couple hundred miles that is higher ground. Look downward too because the geology hare is just fascinating. The adjacent valley was a mile and a half deep canyon in very very modern geologic time. There are massive aquifers under Giza and volcanoes just to the south of modern Egypt. Lake Kivu was in the Nile catchment less than 10,000 years ago. The Great Man-Made River project in Libya might interest you as welkl since this was "obviously the headwaters of the Ur Nile that might have flowed right through your depiction even during the time the pyramids were built.
Good luck. Don't give up and don't believe anything people tell you. This goes a hundred times over for Egyptologists.
As I suggested before; stick to the actual evidence and you can't go far wrong.