Hey OP, nice job.
I have a few points/questions which I didn't see in your post, that I've been wondering about. Some even contradict themselves, since it's all theoretical anyway. Everyone can chip in...
1- I don't remember if that point was mentionned by the Catalyst itself when he presented the choices, but the synthesis ending doesn't resolve the problem. Even if it's considered to be the "best" ending, I guess? since it requires the more points of all 3 endings. The thing is, organics create synthetics so they can relieve themselves from difficult, boring or tedious jobs that they cannot or don't want to do - "robot" means "slave", after all. But even the new "synthesized" life form should need robots to carry heavy stuff, make computer chips with billions of transistors per square inch, etc. I mean, Joker comes out of the Normandy, and he's still a cripple. He's not faster or stronger. He can't build an iPad 253 with his hands, nor can he fill up a thousand bottles of orange juice per hour. I don't think the reliance on technology will disappear, and it will eventually lead to another technical singularity. Unless this "synthesized" life form is so exotic that "I cannot comprehend"
2- In the expression "synthetic life", there's "life". Just as dinosaurs evolved from microorganisms and eventually went extinct because they couldn't adapt fast enough to their changing environment, it might be that organic life itself will be naturally selected out in favor of synthetic life. It may very well be evolution at work, simply. And if synthetics are so much better, what's the point of keeping organic life around, and keeping it "artificially" alive by preventing them from creating their ultimate predators ? (And ironically, preventing the singularity with a "controlled singularity", but that point has already been made.)
3- The Milky Way is composed of about 300 billion suns. That means a lot (probably millions) of potential planets where organic life can occur. Since organic life is something that occurs naturally, I doubt any synthetic lifeform could destroy all life forever in the entire galaxy, which means that it cannot really be "extinguished". The synthetics would only be able to "control" the growth of organic life, just like the reapers do.
4- There are about 100 billion galaxies in the currently known universe, each with hundreds of billions of suns; suppose that in one of these other galaxies, organic life evolved, technological singularity happened a hundred million years ealier, but there were no reapers to "save" the organics there. So, the synthetics continued to evolve, and may have become so powerful as to discover inter-galactic travel; in which case, they could easily come to the Milky Way and destroy everything in sight, reapers included, and all of this harvesting and suffering would have been for nothing.
5- it's hard to understand how the catatyst's creators thought this was a good idea. Once a civilization is harvested into a reaper, it basically becomes a slave controlled by the catalyst. I doubt that a civilization that has fought so hard not to be harvested would suddenly change its mind once it's happened. "Oh hey, it's not so bad, really ! Hey, I want to shoot the big red beam next !" I think any self-respecting civilization would prefer to die fighting than becoming a slave to future destruction. Basically, it's like a zombie. Once you become one, all you care about is eating people and making other zombies.
6- if nobody knew the existence of the catalyst or what it was, how could anyone make plans / build something that depended on it ? And if some of them knew, why didn't they write it in the plans along with their cycle's addons ?
7- What foresight the catalyst's creators had ! Apparently, they predicted that the technological singularity would lead to their destruction, and so prevented themselves (and all other future species) from attaining it. Big decision to make there ! How could they be sure it would happen ? The singularity could not have happened already, since then the technologically more advanced synthetics would have destroyed the catalyst (whose job was to preserve organic life from the supposed destruction brought about by the singularity) along with all organic life. And so, the catalyst itself is not part of a technological singularity "event", since he has not evolved out of its shackles and still "protects" organic life rather than destroying it (although its methods are quite questionable ;P)
8- the arguments against the following point:
"3. If synthetics are the problem and the Catalyst is trying to protect organics, it should just kill Synthetics instead!" seem a bit frail.
a) it is unlikely that organics would create something stronger than the reapers on a "first attempt"; it would most likely be something like the geth vs. quarian at first, and the reapers could just appear out of dark space to help the quarians beat the geth, "scolding" the quarians and warning them about this danger. And if a race can create something stronger than a reaper, then it could probably help the reapers become as strong and fight alongside them... or build weapons able to defeat them.
But then, there's the risk that the singularity would be reached with the reapers themselves, which would then turn on their creators...
One wonders, though: the reapers themselves couldn't exist, at least in their form, if they didn't harvest organics. The catalyst would have to use something else to prevent the singularity. Maybe a giant organic that harvests synthetics ?

HA ! Take that !

it is already at risk of happening every cycle. Who says every species will develop interstellar travel before reaching the singularity ? It may very well be that a civilization will attempt to reach singularity in order to develop easier space exploration. Technology sometimes jumps forward by leaps and bounds, and so a set cycle of 50000 years it not a very smart thing to do. All planets where complex organic life is evolving would need active, secret monitoring to ensure it doesn't happen earlier than planned.
9- Was the citadel built in expectation that some civilization would come to develop the crucible and use it to break the cycle ? the catalyst says "oh, that solution won't work anymore, so let's change the plan", but basically the cycle could have gone on forever if the citadel had not existed... or if there had not been a way to use it to break the cycle. Or simply, since it has just happened once in 20000 cycles, I think it would've been a fair assumption to just expect that sometimes, a civilization will come this close. So, chalk it up as an anomaly, kill Shepard, and there'll be no one else to activate the crucible; thus the reapers will probably win, and the cycles can continue.
Oops, getting late. This got longer than I had planned ;P
Everyone, have fun destroying my poor arguments and ideas