I'm also looking for the same information. I'll be taking my oath next Friday - May 6th and I need an Indian visa by the 15th. Am in NY. I read in a previous post that someone from NY did the whole process between taking oath, getting new passport, the SC and a visa in 3 days.
Reading the NY Indian visa outsourcing company, it seems they accept Renunciation form and visa form together which is a relief. I'm hoping I can get my US passport by the 9th and drop it off to them. But am scared they won't give it back to me by the end of the week and I really have to travel (not to India though, that's later, but I won't have time to do it again).
I thought this immigration nightmare would end with my oath, but it seems to just be endless