Hi Hash Hound
I'm a bit confused as to why you would not want a run off. This would lead you into root rot quickly, Not something you want to happen. It would kill your plants quickly.
The taping of your holes for a few minutes is fine and I think you do get good saturation that way, Don't for get to take the tape off.
In AirPots you want to pack the soil as tightly as you can. If you don't the AirPot will not function as they are supposed to. The roots in the AirPots will work they're way to the holes through the tightly packed soil. Once through the holes they are pruned by air. They die which is OK. That is why AirPots work so well.
Watering AirPots is a slow process. I add a little at a time so it soaks all the way through. When soaked, they have run off also through the grate in the bottom of the AirPot.
I guess putting cloth in a regular pot would slow down the run off and would still work and your roots would finally work it's way through the cloth.
I am lost as to why you want to stop run off, it's good for your plants to have run off. You can also find out if your plants are using what ever nutes you are using is being used by your plants.
Hope this helps you. I would watch the videos on the AirPot site to under stand them better. Good Luck my friend!