Have you thought of running auto's? That would be one solution...
I saw something recently that blew my mind. I was so disappointed I didn't think of it.
The guy had two cmh315's over two large plants. One 315 over each plant. Both plants and lights were in the same, undivided room, and near each other, but the main spread of each lamp was really only covering the plant it was over. But again in the same, undivided room.
In veg, most people do 18/6 lighting. Multiply that X 2 hoods and it's 36 hours. What this guy did (on ig) was run each hood 12/12, but alternated the times. When one lamp turned off, the other turned on and vice versa. So the total hours was only 24. But both plants stayed in veg. Also, when the light above the plant was out...the plant had that "lights off" look about it. So he was using 1/3 less electric, keeping them both in veg, and they still appeared to be resting during lights off.
I assume when he flips, he just syncs the timing of the two lamps.
Not sure if that helps. Anyway...
Does my supplemental lighting need to be strong or just enough to keep the plants awake?
See above. I've not tried what you are attempting, but in order to flower, the plant needs uninterrupted dark time. If it's light enough that you can see clearly, a sound plant will stay in veg. It doesn't have to be bright, but it has to be visible. Think rainy/cloudy day levels of light. Since you are in Cali, you might have to google what that is like ; ) You should be able to walk around in the space w/o assistance, If something was on the ground, you should be able to make out what it is...that level of light.
Would the plants possibly reveg during flower?
If there is only 11 hours of light, no.
Would there be enough sunlight/hoursduring winter to get some good bud with nice yields?
I don't know what your winters are like...but if you have 11 hours of daylight and proper temps etc, it should be fine. You would get moderately better yields with 12 hours of daylight during flower, but imo, it's not worth the extra work. Just take what mother nature gives you.
The only problem I can see is that if the veg stage light isn't strong enough, the plant won't veg very fast. Which is fine. It's better than nothing. But you asked about the light intensity. It doesn't have to be intense to keep them from flowering...but if it isn't strong, the plant isn't vegging as fast as it could, which will affect your yields.
But auto's or the way you were describing...I wouldn't hesitate to try it. I think maintaining the right temps will be the larger issue.