It would not have been that hard to fix this, honestly. Just a tweak or two to the dialogue and a slightly different VFX shot.
Enterprise was shown to be at full stop and then suddenly plunges towards the Earth which would be about four days away at the distance they're at. The Enterprise had such severe damage that gravity is failing, the very last thing to go when the ship is being blown to pieces. She clearly didn't have any thrust behind her one moment, and then the next a lot of force was pulling on her...
So, here's how I would have fixed the issue. It's a very simple tweak. Enterprise would still have a little impulse power left. Not enough to escape Vegeance's firepower. When Spock said they can't flee i'd just have him say instead "We have no weapons and only minimal impulse power, not enough to escape." When Spock does his trickery on Khan, he has Sulu engage impulse engines to get away from the blast zone. The ship just isn't fast enough and the explosion ends up pushing on the ships stern, plunging it into the atmosphere. We'd see the shock wave literally smack the Enterprise into it's descent.
Simple.
Enterprise was shown to be at full stop and then suddenly plunges towards the Earth which would be about four days away at the distance they're at. The Enterprise had such severe damage that gravity is failing, the very last thing to go when the ship is being blown to pieces. She clearly didn't have any thrust behind her one moment, and then the next a lot of force was pulling on her...
So, here's how I would have fixed the issue. It's a very simple tweak. Enterprise would still have a little impulse power left. Not enough to escape Vegeance's firepower. When Spock said they can't flee i'd just have him say instead "We have no weapons and only minimal impulse power, not enough to escape." When Spock does his trickery on Khan, he has Sulu engage impulse engines to get away from the blast zone. The ship just isn't fast enough and the explosion ends up pushing on the ships stern, plunging it into the atmosphere. We'd see the shock wave literally smack the Enterprise into it's descent.
Simple.