Yes, OBMM has BSA redirection Active. I didnt try the timestamp thing, what is that?
In the Utilities section under Arcive Invalidation there is a button that will cause OBMM to reset the dates on all Bsa files so an individual mesh or texture will be allowed to overwrite its "twin" inside a Bsa file, many mods with meshes and textures can have thier changes prevented from working in the game if you load a mod with a Bsa after the mod with the meshes and textures.
This is also the reason many smaller mods will say "install last to ensure this mod will work in your game", especially mods made by someone new to modding.