I have a finished basement wall that has an exposed header since removing a drop ceiling. My goal is to replace the ceiling with a flush ceiling, perhaps drywall or a joist-mount grid system. The way that it was blocked to the joists would not allow for a flush installation, so I'm going to fix it. Access to the other side of the joist is only through the slit you see in the picture below, and the next joist sits on a concrete wall for my basement. Is there a way to attach the wall that will allow me to remove this block? Perhaps with some drywall damage, could it be installed to the concrete wall? Can I use a bracket of some sort that can be installed through this small area?
I am assuming that this blocking is help stabalize the framed wall on the basement walls. Normally the blocking would be inside the joists so that the 2x4 is even with the bottom of the joists. Your wall was not put up this way.
Therefore your new ceiling is that low. You could cut out the 2x4 blocking, install like I said and add another 2x4 under all the way to the drywall and this would stabilize the wall - if done a few times per span.
However you have not much to attach drywall too. So you would also have to add vertical blocking every couple feed and add more drywall to make this right. If all of your walls are like this... sorry. This is a full days work considering the drywall and extra mud and tape. And even doing this isn't the "right" way. Your walls should be touching the top of the ceiling for lots of reasons.