That's a beautiful fence! We have neighbors from heck and I put up a bamboo fence on the gate as they would routinely look down our drive to see if we were home.
A few possible solutions might be (depending on your situation) to (inside your fence) reinforce the bamboo by adding lumber as a backing so that it'll block out the light (but it won't look as pretty obviously). If you can find thinner bamboo you can bundle them together and then add them to block out more light. Rhamnus (sea buckthorn) may work though I don't know if that's ever green or not.

I got climbing roses and hydrangea, but decided that those would not cut it for this purpose since they would provide minimal coverage during winter. I also got some straw bamboo to add coverage behind the fence, but the straw bamboo is useless. I plan to use it as a trellis rather than as any kind of fence. I'm fairly certain that is the only use for straw bamboo other than building chicken pens and cheaply identifying the boundary between the beach and a beach house.

I decided to put golden euonymus in front of the fence, and I may either put a trellis behind it for it to climb up, or simply train it to go up the fence. The good thing is that euonymus is one of the few evergreen scrubs with a reasonable ability to climb. It will require trimming and training, but that would go for any scrub in this situation. I am interested in finding what alternative evergreen options there are for this situation. Holly seems to be another options, but euonymus seems to be ideal for additional fence coverage. In fact, it sounds like euonymus and a trellis could constitute a fence in itself.

There may be some thujas that may fit back there, not Green Giant of course, but there are some cultivars that don't get quite as huge as GG does. Good luck with whatever plants you go with, hope the Euonymus works out!

Nice one. You can use thin bamboo stick or wood to block the light. It will definitely solve your problem.