Good thoughts Anthony,
I think the first-time reader probably assumes the crebain are sent by Sauron. He knows that Sauron is reported to utilize birds and beasts as spies. He knows that Rivendell is worried about Sauron's spies. He doesn't know that Saurman has any spies, nor any ability to command birds.
I think that readers who read on might eventually consider the possibility of Saurman having sent the crebain. However, we never see Saruman using them again, when it might have been useful for him. So, I think Sauron sending them remains a more probable hypothesis. Particularly, as we see a possible Nazgul on high in the next few days, and an attack by wargs, both of which are more associated with Sauron than with Saruman. So, if Sauron sent wargs and a flying Nazgul over Hollin, it is quite likely that he also sent the crebain.
Hypothesis: The Nazgul report back to Mordor in early January, after returning from disaster at the Fords of Bruinen. It is only then that Sauron knows that the Ring was in Rivendell. He does not have spies near Rivendell (as confirmed by Elrond's scouts). He needs spies there, and covering routes from there. He mobilizes Nazgul (now mounted on flying beasts), crebain, wargs, and other spies and sends them to Rivendell. On the way there, they will spy out the land. Some will remain around Rivendell to spy. Some will then scout the exit routes from Rivendell that were not covered on the way in.
If Saruman wanted to send out spies, why wait until January to send forth crebain? Gandalf escaped from Orthanc in mid September. Surely if Saruman had genocides of crebain to send out as spies, he would have sent them in September to blanket the Shire, the roads out of the Shire, Rivendell, and Lorien. The crebain not moving north until January seems to me to indicate it more likely that Sauron sent them after being alerted by the Nazgul after they struggled home to Mordor, that the Ring was last seen in Rivendell.
The timing seems to me to indicate that Sauron, rather than Saruman was the more likely commander of the crebain as spies.
I follow your logic.
A first-time reader isn't aware of a simple Sauron/Saruman dichotomy of opposition powers here.
There's no reason presented in the text that there couldn't be a third power that has previously been inactive:
Maybe Treebeard sent the crebain from Fangorn? Only a re-reader is aware of Treebeard, and recognises the silliness of the suggestion.
An ambitious Elf that disagrees with the outcome of the Council? There's been time to organise things, and following the party directly from Rivendell would be too suspicious.
An ambitious crow that overheard 'others' talking about the Ring and was tempted into making an attempt at possession.
These all seem silly by varying degrees to re-readers, but a first-time reader, with only the Hobbit (at most) to judge by, might consider some of these (and others I haven't thought of) perfectly possible.
All of that said, timing alone is insufficient to discount Saruman. The crebain can be Saruman's to command with the timing of their dispatch coming from Sauron.
Sauron could have dispatched the Nazgul and the wargs up the eastern side of the Misty Mountains, and told Saruman to be on the look-out for spies coming from the north on the western side (not mentioning the Ring, of course), and Saruman then sent the warning on to his Dunlending vassals. One or more of these vassals could have people that have trained these birds to a limited degree, which Saruman then took advantage of to perform the search guiding it with his will projection techniques (that we see used during the pursuit of the orcs across Rohan.)
If these are Sauron's spies why did we hear no reports of them around Gondor at any time?
If these are Saruman's spies why did we hear no reports of them around Rohan at any time?
Maybe they were there (in one or both places) and no reports were recorded; or these birds were perhaps used for this one mission alone.
Perhaps they flew until exhaustion and death; or when the search was completed they were released to their own devices, and there was insufficient food in the area to keep them all alive, resulting in a mass starvation; or they returned to the forests that they came from, having been considered of no further use.
My main point in all of this is that while we can develop theories to explain what we see in the text, there is insufficient evidence to declare one as the real explanation, and a first-time reader doesn't (yet) have most of the evidence we have.
So in the absence of 'one true explanation', what does the reader have? A sense of doubt and uneasiness that matches that of the company.