I did some digging about the OPs rant, and discovered why this may be more complicated than the typical rebooking.

The BOM-LHR flight on VS now does not land in LHR until 4:35pm, which is indeed too late to connect to any LHR-US flight on either Virgin or Delta that would allow a connection to BNA that night. Hence why OP now has an overnight layover.

While OP makes a point that this is a 36 hour trip, this was always going to be a long trip.
The only shorter options Delta is selling leave Bombay at 2:35am and involve flights on Air France, or 2:30am on KLM. (With routings many of us would find *worse* than the overnight in LHR!) During a holiday week, there may be limited availability on these flights.