Can I perform a large ceiling drywall repair myself?
Yes, this is certainly doable, but I guess an assistant would be very useful when handling pieces of drywall and attaching them to the ceiling.

What you essentially will have to do is remove the affected drywall (not necessary to remove entire sheets - if a sheet is only partially damaged you can cut the damaged part away and leave the unaffected part) and then patch the area. No major difference compared to a small area patch - you will have to replace the damaged material entirely from one closest stud to another, studs are separated with rather small distance.

This will constitute lots of tedious work and will be rather dirty but it is certainly doable by a DIYer.