I swear this thread has made me straighten out my own personal marauder-era timeline. How I missed this. -sighs-
The hilltop scene could've possibly taken place anytime between 31 July 1980 and 23 Oct 1981 (a week from Halloween with both dates thoroughly extrapolated). Voldemort shouldn't suspect Snape if Snape were to handle things as evasively as he always does. Snape was employed at Hogwarts at the time L/J died. This is canon. Voldemort might actually find it hard to believe that Dumbledore gave Snape the job. It'd go to show that Voldemort doesn't do much rational thinking, does he and merely enjoys ways to get retribution over Dumbledore. But if there's something about Voldemort we know, is that he underestimates others. Time and time again, he's mocked Dumbledore for his theory about love and it's not just love is it? It is about having trust in people and giving them the space to really chose what they want.
I believe Dumbledore trusted Snape's motive to help and that made him worthy of a place as the Order's spy. But offering the place at Hogwarts was an extention of Dumbledore's plan that I think by no means would have happened that night on the hilltop. There is a possibility that it might not have happened for sometime after. Timing is what derives plot in marauder era. Dumbledore must have needed time to think about Snape's loyalty, devise ways in which Snape could help them without alerting Voldemort's suspicions. Even plan decoy missions, so that Snape would bag Voldemort's absolute trust.
If Snape delievered this, which he has proven countless times during the series he can, I don't think Voldemort will be any wiser.
Why I find the complexity of secrecy amazing is that Dumbledore and Snape seemed to know almost everything about who was who (except for Peter of course), but the Order members? Sirius says in POA 'what's Snape doing here?' Shouldn't he know because Snape was teaching there before Sirius got sent to Azkaban. But okay, maybe he couldn't know because do you really keep track of who's teaching at school once you've left?
In GOF when one of the trio mention Karakoff showing something on his arm to Snape, Sirius in Padfoot's Return is wondering what that might be? Did Jo really mean to say that the Order members or first war Order members should I say, did not know about the DE's mark on their arms?
Also, it seems Snape was spying for Dumbledore for at least a few weeks or more before Halloween, yes? There's a reason I believe Peter was just a lowly informant here and not a full fledged spy. If Peter was in the inner most circle, there's no way Snape might not have known about it. Sirius would think he'd been spying occupationally for Voldemort for over a year before Lily and James died because he's had time to think over everything in Azkaban. Sirius in his isolation and hatred would've found a way to link every leak of information during that time back to Peter. And maybe it was true. But there's this whole chance that Peter was actually blundering this whole while so scared he didn't know how to stop.