Re: Attaching baseboard to concrete wall
If it is full thickness 1x base, you can use expanding foam to bond it to the masonry, and it will set in less than an hour, so bracing is minimal. I do this technique a lot in historic restorations where the wooden deadman inserts are long gone. If you have subfloor exposed, use 90* triangle blocking screwed into the floor to keep the baseboards perpendicular. On a finished floor you can use hot glue instead of screws, just tap the blocks off with a mallet to remove.
Drill two 3/8" holes every 2 feet or so to have a place to insert the foam "straw".
Remove not the ancient landmark, which your fathers have set.