Unless there are layers of glue-applied wallpaper to remove, it's uneconomic to r&r drywall rather than repairing it. Electricians are masters at fishing new wires where needed. Plus, what your estimate is missing is that the old smash- and-shovel-it approach is no longer prudent or, in many cases, allowed, when it comes to removing lead painted drywall. (Though you'll likely soon hear from someone who says, "lead, schmead, so what's a little dust gonna do ya?") Here is a link that might be useful: What Home Owners Should Know about Lead-based Paint

I am not-repeat not-a professional or expert, just a homeowner like yourself. Jost some ideas.... The edges: If it were mine, I think I would just tape and mud the wall and ceiling as best I could, and then cover the wall-ceiling joint crack with a crown molding or maybe even just some quarter-round stock. Light fixtures: On This Old House, when they have to make this cut in drywall, they use a special power tool with a spiral cutting bit that look like a drill bit, that guides on the inside edge of the metal fixture mounting box in the wall or ceiiling. Looks like you did this by hand with a keyhole saw or something similar. From what little I know about it, I'm not sure you can fix this with tape and mud. Again, if it were mine, I think what I would do is go down to Lowe's and buy an inexpensive plastic ceiling medallion, just big enough to cover the ragged part, and install that above the light fixture. It may be a bit "grand" for what looks like a pretty small room, but it's a lot less trouble than tearing out the ceiling and trying again.

Maybe I'm missing something, but to me, the area in your photos looks more like an attic than a dining room. Whatever. One cheap way of patching damaged old-house plaster ceilings is to cover them with drywall. Old house lovers cringe when they see that done, with good reason. Usually the house deserves better. (I say "usually" because in houses old often means well built, but not always. I've run across a few old houses that were thoroughly undistinguished -- just old.) Before you tear down that drywall, you may want to contact a professional plasterer (if you can find one locally) and pay him or her look at the situation, to get an idea of what you might be in for. As for knob and tube wiring, don't automatically be afraid of it if you find it in a ceiling. If it's been properly maintained (no oversize light bulbs, not buried in insulation), it's often still reasonably safe for lighting circuits. Still it's best to replace it when you can, certainly if you have the ceiling open for other reasons. That's in part because age and air pollution have not been kind to the rubber that insulates it.

It's an awful situation because he sounds like a jerk, but I would leave it.  The risk of damaging things and making it worse just aren't with it.  For example,  if the crown molding cracks,  they will probably just use wood filler to fix the crack. Would you be happy if you could see a bit of where they had to fill?    As an analogy, we had a large jetted tub get damaged during new home construction.  In that case, the builder pushed to get it repaired on site.  He said he was willing to replace the tub, but was concerned with what else could be damaged as they rip out the surrounding tile and remove the tub through the entire house.  We ended up being happy with the repaired tub and have had no issues with the repair not holding up.