Strapping for 2x4 before drywall?

Ceiling in bay window is cracking, looks like right along the bead on the header outside corner (I think that's what to call it). I chipped off a bit along that line and it looks like they didn't tape over the bead, but there also seems to be some give in the ceiling drywall, like it's not fastened to the joists really well. I searched for nails/screws, and can only find what I've marked with red in the last picture. So from that, I think I can tell where the joists would be - I've done lots of knocking, but am having a hard time hearing any difference in sound. I know I can put a small nail through to confirm, but thought it wouldn't hurt to ask here before I go putting holes all over the place. Can I be pretty sure that where I've marked in blue in the last picture is where the joists are? Any others that are typically in a bay window? Feel free to draw in.

I just put up faced batt insulation for my garage ceiling, joists on 16 inch centers. I am seeking advice on ceiling finishing material not having the weight of drywall (1) questionable whether the joists will support that plus some stored materials up above and (2) don't want to wrestle the drywall ovehead and onto the ceiling.