I’m not sure that sweet spot exists, and a lot would depend on composition and entry angle.
Using ice would take a lot less energy to blow it apart on reentry.
Ice would be ideal for a number of reasons; a shield you could then use for water, air, and fuel! To get a big enough chunk though, you'd probably need to send drones to drag some icebergs from around Saturn. That... would be something! Doable, although probably very expensive, it would share tech with asteroid mining so maybe there's hope for it.
You guys are aware that you're basically describing the plot of Seveneves?
It's a great book, but in terms of the science, it's not new. Dragging mountains of ice from Saturn or something similar is a sci-fi cherry.