I finally was able to catch the Regis Pokemon. Funny thing is is that the day after I posted my whine about not being able to catch them, I caught them all quite easily.
It really does just take patience in order to catch them. I was successful catching them by getting their heatlh down to almost nothing and then using “Sing” or “Sleep Powder” to make it easier to catch them using either “Timer” or “Ultra” balls.
Unlocking the ability to catch each one is a little tricky though. Follow these steps or read the FAQ over at GameFAQs and you’re good to go.