Need help with plant choices for hot shade

This is not really a design issue, but I couldn't figure out which forum to post in, so here goes.

I live in the middle of the suburbs surrounded by two story houses. My back yard is mostly concrete driveway and lawn with a couple of small garden beds (was like this when we bought the house). There is a patio at the rear of the property that is surrounded on three sides with garden beds that at most are only 3 ft deep. The 4th side butts up to the lawn. The soil is clayey-sand. These garden beds are also surrounded by 8ft fences on 2 sides and my garage on the 3rd side.
The property faces south-west and the back yard has an amazing micro-climate that is much warmer than surrounding areas - in summer we frequently get temps up over 85. It's also quite sheltered from the wind.
My neighbour to the rear has three awful trees that extend over my garage. These trees and the garage cast shade over the patio and gardens until a couple of hours after noon. My neighbour to the left has an evergreen magnolia, part of which grows over the fence line, casting more shade from noon onwards. So, in a nutshell, the beds on the left get mid-morning sun until 1pm-ish, the bed on the right gets sun late in the afternoon, and the bit in the middle gets sun for a couple of hours either side of noon. No part of the garden is in full sun.

My problem comes when trying to find plants that will suit those light conditions. Shade plants don't work in the bed on the right because they get fried in the late afternoon sun. The plants in the middle bed need to be able to handle hot midday sun and shade for the rest of the day. Can anyone help me work out what kind of plants would be best suited to these conditions? Unfortunately ripping the driveway and lawn out and relocating the gardens to the center of the yard are not an option at this time, much as I'd like to. ;-) That will take a little time and gentle persuasion to convince my husband. I've read numerous books which tend to suggest plants for morning sun and afternoon shade, not the reverse.

I drew this picture up in excel which I hope makes things a little clearer. I've also cross-posted this in the Shade Forum. Thanks for looking.