Hi Fj, I garden in the cool Pacific northwest so I am not familiar with clematis that grow well in hot climates. After reading these posts for the last few years it seems like clematis with viticella or texensis parentage seem to do well in hot climates. These are type 3 pruning groups. An east exposure would give your clematis enough sun to bloom and shade it from the hot afternoon sun. You could plant early and late blooming type 3 to give you bloom time over the whole summer. Also a lot of gardeners will cut back their clematis after it blooms in order to get another flush of blooms. Clematis like lots of water and fertilizer to bloom well. The clematis would easily grow up the trellise and onto your shrub. The type 3 you can hard prune in the fall so you don't have the dead vines on your shrubs all winter. There are hundreds of varieties to choose from. You can go to clematis on the web and search their database for flowers you like. You can put in the color you want, the pruning type, the group(late large flowering, etc.)and see what comes up.

Here is a link that might be useful: Clematis on the web

SF Bay area is more like the NW than a hot climate. Though frost is rare it is often foggy and cool.

I would think texensis and viticellas would be likely to mildew as they do here.

Type II's often will bloom twice, once in spring and again in fall. Daniel Deronda is a purple that reliably blooms twice for me without extra pruning. Multi-Blue is one of my faves as well.

I don't think any Clematis color would clash with your Agapanthus. Just choose what you like. Going to a reputable local garden center and asking what does well in your area would be a good idea. Not Home Depot. Also keep your eyes out around town. Is there a Bay Area forum here?