Farfetched and out of line with the Time Crash, but that made me think of anti-annihilation energy somehow stopping the destruction or shunting of past timelines to the Darkness Beyond Time when history is changed. The crazy application is that perhaps this played a role in giving birth to Home World as a separate dimension, when Kid's time-change should have merely shunted Another World's 1010-1020 A.D. history to the DBT with no other effects. So, tenuously, perhaps the Time Crash's anti-annihilation energy was directed towards that point in time for some reason (ah, we're in left field here), or, the Frozen Flame (which seems to be a source or conduit of this energy) was used in 1010 A.D. to create Home World from Kid's change, perhaps activated deep within FATE as part of Project Kid.
To justify that anti-annihilation energy reverses that timeline-shunting effect, well, perhaps the Counter-Time Experiment needed that so Chronopolis wouldn't accidentally overwrite history in the past and negate itself out of existence. Although really, creating a new dimension isn't exactly "controlling time", since they'd be separated from their achievements.
Bah, that's all too speculative.
Actually, I always assumed that the anomalous nature of the dimensional split was a direct cause of Chronopolis' counter-time experiment. Belthesar planned everything from the start, after all. So, it's not too far fetched at all in my opinion.
As far as "controlling time", I always thought that what they intended to do (although this is not supported from the story script), is to create a pocket dimension around Chronopolis using Lavos' energy, in the same way that Lavos creates a pocket dimension around itself. In this way, Chronopolis would be removed from the space-time continuum and have full access to ALL time periods, thus "control over time". However, something went wrong and instead the boundary around Chronopolis was connected to 12,000 B.C., rather than being disconnected from every point in the space-time continuum.
I always also assumed that "anti-annihilation" energy was just a pseudo-sciency way of referring to anti-matter, because wasn't it stated elsewhere in the plot that the Neo Epoch ran on positrons or something of that nature?