Thanks for the pointers guys, I got my Notes back!
Here is what I did:
I had a backup of my iPhone on my computer. So, I decided to restore my phone from this backup using iTunes - only to see all the notes in Notes come back but then vanish just as fast. I realized that this was because I had actually deleted my notes from iCloud and even though a copy existed in my local backup, they were getting deleted once the iCloud account on my phone synced up with Apple. So, I removed the SIM card and made sure none of the WiFi hotspots that my device could connect to, were reachable. And then I did another restore from backup. Now because there was no connectivity, my phone's iCloud account couldn't sync up with Apple. Hence the notes stayed locally on the device. Then, I went to Settings > Notes and enabled "On My iPhone" Account. Then, back in Notes, "moved all" the notes to this local account. Re-enabled network connectivity and moved the now "local" notes back up to iCloud - and all is golden. Did learn though not to be in much of a hurry before "deleting"... Ooh happy days are here again!!