Given that your builder offered a half-assed solution, I think your next step is to talk to another qualified insulation contractor.  Ask them how to go about fixing the issue such that you have the same quality had it been done correctly in the first place. Tell them you don't want the cheap or fast option, but the best option to fix it properly.  Get a detailed write up, pay for their time to write up the estimate if you need to.  If you don't like what that person offers for a solution, try another.

Once you have another qualified insulation person giving you a solution you like and cost, take that back to your original builder and ask them to do the work or give you a check so you can pay for the other contractor to do the work.  If you get an attorney involved, they'll like having this second opinion/estimate from another contractor as well to use as leverage.

On my shop, there was Tyvek covering this area between headers on the tops of the wall.  When they sprayed the walls they didn't spray the bottom side of that Tyvek in the cavity you show in your picture.  I asked why, they said they would do it from the top side.  I'm guessing they really just missed it, and were too lazy to correct it at the time.  Later when they sprayed above the ceiling, they still didn't get this area covered well. They then brought in a froth pak and crawled around on their hands and knees to spray that area again from the top side.  I didn't have the blown insulation in yet.  You do, but that can be vacuumed out.