Spicejet - Reschedule the flight in couple of days after the ticket booked

I booked tickets through Goibibo from Shirdi to Goa for Jun ** ****. I got a few choices of flights. I choose the flight from Shirdi (Spicejet with a departure at *:** am) to Hyderabad and then a connecting flight from Hyderabad (Indigo with a departure at **:** pm). A few days later I get an email from Spicejet which said, the flight from Shirdi got rescheduled to start at **:** am with an arrival time at Hyderabad as **:** pm. Because of this, I missed my indigo flight to Goa.
I reached out to Goibibo on their phone number multiple times on April *st **** (asked them to call me on my USA phone number) and spoke to several customer representatives who referred to open a ticket. Some of them were not helpful (they said they called and that I am not picking the call whereas, I never received a call) at all but a couple of them were really helpful. They opened tickets and they mentioned I will get the full refund from Spice and that they can't help about connecting flight from Hyderabad and I have to reschedule or cancel incurring charges. After persuading them to talk to SpiceJet on my behalf, Goibibo personnel came back saying SpiceJet rejected the request to cancel with a full refund since it's not a * hr reschedule. Now I went to indigo with the request for a full refund explaining to them what happened. They said I will have to cancel or reschedule with charges (the money I will be getting back will be Rs ****+ while incurring charges which includes Goibibo charges up to Rs*****+). They were not in a listening mode to my reason.
Next day a person named Saifali from Goibibo called me saying he is the manager and after lengthy discussion, he said he will get back to me after talking with higher-ups in Goibibo and try to resolve my issue. Till date, I never received a call.

In the meantime, I sent an email to Spicejet, Goibibo, indigo. I got a response from SpiceJet telling me that it will incur charges for rescheduling or cancellation and they can't go back on that. No response from indigo and Goibibo. The email said that email id is not monitored.

I reached out to all three of them over twitter and Goibibo was the only one who responded. They opened a case. So in total, there were three cases. At the end of the day, Goibibo responded to the first ticket saying they can't help any more as they are just agents.

I also tried seeing alternate flights by rescheduling my Indigo flight from Hyderabad to Goa but I couldn't find anything till the night (the earliest I could find was with indigo at around * pm) which means I have to stay in the airport from afternoon till * pm night with family of two kids and a senior citizen doing nothing. The only way for me is going to Goa from Shirdi through Mumbai (this route is available) so that I can reach out by * pm afternoon on **th June.
I am trying to figure out my options and probably want to approach consumers forum with this. In the meantime, I haven't cancelled anything and the tickets prices are rising. Hence need to move faster on this, please.