I had an idea to make the AIs stronger. I could be entirely wrong about this, in which case ignore this.

What I was thinking is: Couldn't you code the AI so that it will build a certain building/unit with a very high priority (especially Supply Depots/Pylons/Overlords) when it has a certain unit? If so, you could set it so that it does so if it has a special unit it couldn't obtain normally (eg. a Mineral Field), and use a trigger to create that unit for the computer player? Then you have a much greater degree of control over the AI's actions. Am I right, or am I stupid?

Yes this works and has been done. It also works the other way around using the AI script's create_unit command detected by triggers.