I've noticed that AI ships in a blockaded port seem to frequently manage to escape past my cordon, meaning that I have to break the blockade to go chasing.

Its a pain in the ass.

Blockaded ships should have to do battle with the blockading fleet before they can escape.

Actually what I think is happening is that the AI does attack but then withdraws & thus get moved away.
That being the case, there should instead be a high chance that they withdraw into the port not away.