ITT: fans demonstrate, once again, how little they understand the Reapers and the central conflict.
The first problem was the question: commander, fleet, strategy. None of those apply. You guys need to get the "War" idea out of your heads here. To us, the organics, this conflict is a war. To them, though, it is not. That is not how they are approaching it.
The way to think of the Reaper/galaxy conflict is more like this: the Reapers are like a team of (human) construction workers and city planners are IRL, and the galaxy is like local fauna in their way. The animals may see the rise of a city around them as an attack on them, but the truth of the matter is, the humans do not really give a **** about them or their habitat. They just want this city built.
And sure, the humans will sometimes take measures that specifically target moving the animals out, killing them off, or destroying their habitat. However, it is typically never priority in the big scheme of things.
... Which brings me to my next point: guys, the Citadel can close. The Reapers will be seen coming from miles away. It is also the one thing that most species of the galaxy (the major players, at the very least) will quickly band together to defend. The Reapers would suffer as heavy casualties as they ever would in a cycle, and likely not even succeed.
... Which brings me to my next point: a Reaper is not analogous to a warship. It is, to them (using their words), a civilization. The loss of a Reaper is not a small matter. So saying that they should throw themselves at the threat to end it would be like the owls saying "stupid humans, if they just nuked this entire city then we would seize to be a problem to them any longer -- clearly they have no concept of war!" (never mind that the whole plan would fail if the Citadel arms close).
Finally, it should also be noted that the Reapers had no reason to believe this cycle was ever going to pose any challenge before the Crucible was revealed to be a thing, so there was no real reason for them to throw themselves at the Citadel rather than wear us down over time in a war of attrition. Hell, one could even have argued that the Crucible should not have alarmed them because no one was even sure that it would stop the Reapers.