How many hours of sun are the plants getting?

Mike

Like four hours of direct sun, probably about 8 hours of reflected sun

You shouldn't need to. During just those 4 hours, they will be getting ~16 mols on a sunny day. Plan-ts grow great with a total of 20 mols a day.

Mike

I did this and it was beneficial, but sunlight was a little more limited than yours. It's easy enough to hook up an outdoor MH or HPS floodlight to shine down on your plants, but remember that a 400 watt HID light (the strongest I've seen for outdoor use) will only illuminate about a 5 foot square area, and must be mounted a few feet above your plants. I had some hassles with neighbors, too; you can buy hoods to cut the light off at the edge, and of course the lights will only be on during the daytime, but some people may find a reason to complain whatever you do.

I'd try it for a season with what you have before spending money on the lights and electricity.

Here's an example of what you can do with outdoor lights in shade. Click on the picture for more details.