CSIF will not let you in more than 4 hours early. I think there is a good chance that IT will through-check your bag, especially if it is on one PNR. So, my suggestion is to take a cab/car from the domestic terminal to one of the hotels near the international terminal. 4:00 PM is before the worst of the traffic, but it could still take easily 30+ minutes. Have a late lunch/early dinner at the hotel, and then head to the international airport around 8 for check-in. (None of the lounges in BOM are that nice.)