I think it's utter silliness to think that Gandalf actually wanted to go through Moria--he's not so coy that he would carefully manage things like that, he would have stated from the start "let's go that way." His choice of paths was pretty clear from the start: the Redhorn pass and, failing that, Moria as a second-best but not great option.
As to why he rejected to two more northerly routes, the reasons for that have already been stated here: too many goblins, too long close to Mirkwood, too close to Dol Guldur.
But I think there might be another interesting reason why he wanted to try Caradhras...it was the only route that they could have followed and then skipped going into Lothlorien. If they had been able to get through the mountain pass they would have been able to keep Bill (and thus the supplies he carried), come down the stairs (and thus had a much easier road somewhat further to the north and thus not quite directly into the forest) and they would certainly have been in better shape (not having had any to-be-expected encounters with goblins). They might then have held a course north and around Lothlorien, or maybe even snuck by on the western border between the forest and the mountains.
Why do this? Perhaps, just perhaps, Gandalf had some secret inkling of the danger Galadriel posed to the Fellowship. She darn near took the Ring from Frodo and she certainly consternated the rest...maybe Gandalf had it in the back of his head that if they could slip by her realm unnoticed, that might not be a bad thing....
Going through the Gladden Fields almost guarantees that you are going to spend a long time mucking about on the borders of Lothlorien and in the surrounds and thus attract more Elvish attention. Taking the Ring that close to both the Witch King and Galadriel, for that long, might not have been much to his liking....
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Scribbling scrabbling.
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