I think 305 AD might be too late. The problem with Tetrarchy was the personalities involved, and by that point they were too entrenched to think of anything other than trying to claim supreme power for themselves. Without Diocletian in power, the Tetrarchy was going to fall, and it was only a matter of when, not if.
Now, one way to make it last only slightly longer would be to have Constantius Chlorus live for a few more years, and perhaps some other dynastic events resulting in a more balanced dynastic equilibrium existing, but even then, it was only a matter of how long the fragile balance could be maintained. The moment either one of the Tetrarchs post-Diocletian showed just a little weakness was the moment the others would attempt to jump him and divide the spoils, dynastic alliances notwithstanding.
In other words, we need to create a relatively evenly matched group of four Tetrarchs, some of whom are, by the way, advancing in age, and may not survive long enough to make it for the full 20-year term. Even if somehow miraculously the new Tetrarchs make it through their entire 20 year term, what would make them relinquish power? Without Diocletian, there was simply no other personality that would be willing to part with power voluntarily. And even to get to that point would require some serious ASBs in my opinion.
More likely scenario would drag the Tetrarchy out for about another 2-3 years at most, and then it would collapse pretty much how it did in OTL. If you want to make it last, you will need to go much earlier, perhaps to Diocletian and the beginning of his reign, to reform the system so that it did not need a strong autocrat calling the shots like Diocletian did, and so that it can continue functioning even when Diocletian himself is no longer around. And the end result might be a vastly different division of Roman Empire...