To set the scenario, we're talking about the orbits which ball bearings would end up in if you had a cardboard box full of ball bearings in a stable, circular low Earth orbit, and you set off an explosive in the middle of the box to scatter the bearings. You're wondering if the ball bearings that the explosive happened to launch prograde would end up in a stable elliptical orbit with a higher apogee rather than re-entering the atmosphere.

I'm not that strong on orbital dynamics, but I think the answer is that you're right. The ball bearings launched directly prograde would be in a new stable elliptical orbit with the perigee at the explosion point. That means I was wrong about the debris only affecting the orbital altitude where the explosion happened. But most of the ball bearings would still re-enter the sensible atmosphere within a single orbit.

The Δv required to deorbit from LEO is surprisingly small. In https://www.nasa.gov/wp-content/uploads/2024/06/iss-deorbit-... we find that deorbiting the International Space Station to a controllable place in "a remote area in the ocean" from its current 415 km altitude requires only 57m/s of Δv. The more precisely controlled Space Shuttle re-entry used 90m/s of Δv: https://space.stackexchange.com/questions/33172/calculating-.... It seems crazy that a change in orbital speed of only 1% would be enough, but there it is. There's a lot of explanation in that SE question.

The ISS document also explains that even the enormous ISS will deorbit by itself in "roughly one-to-two years without reboosts", which is why most LEO satellites are in somewhat higher orbits.