I would take down the cedar frame and clean the block up as best you can removing all loose material and dust/dirt. Build your new frame and install it at the top and bottom like you want. On the side maybe put some bolts sticking out with the nuts holding them tight on the back to the frame with the ends bent a little. After this is all done mix up some mortar mix and fill the gap completely. If the areas are tight you may have to use a cake makers pipe bag an squeeze it in. Then when the mix dries it will dry around your bolts holding the sides into place.

I have seven acres and plan on building a house sometime in the future. I plan on making a vault like you are doing. But I want to make the room and then just buy a sentry style gun safe and mount it in the wall about a foot off the ground and then just cut the back off. Should look cool and work great.