The first thing to do is a soil test. Since the Hollytone seems to at least temporarily improve things, some nutritional issues would seem to be involved. Perhaps pH as well.

Your sense that the sun is a part of the problem is likely very accurate. The intense heat of the sun even in winter in a southern exposure causes chlorophyll destruction in the leaves. Foliar sprays will not help with this, nor will the extra nitrogen in any form, such as the cow manure (best avoided, anyway.) Low humidity makes the problem worse and usually will cause sections of the leaves to brown and die.

You may get some improvement if the soil test indicates nutritional deficiencies, but it's always a challenge with rhododendrons to supply enough sun for good bloom and enough shade to avoid leaf damage.

You covered a lot of issues so I will address them as you mentioned them:

"The main problem, though, is that they turn a very sickly shade of green in the late winter; they seem to darken to a more normal shade after I fertilize with Hollytone in the spring. Basically I am unsure whether the color is 100% a nutrition issue, or whether (as seems more likely) sun stress is contributing, too. I haven't tested my soil yet and need to...anyway, its composition is EXTREMELY sandy and probably is deficient in easily-leached out minerals/elements. I also ought to know my soil pH and I don't...Lavender grows very well in the same area, though, and I know it likes an alkaline soil. That's not good for rhodos, I know."

I think your rhododendron is living from Hollytone to Hollytone and due to the sand, nutrients are leaching out A uniformly pale green is a lack of nitrogen. I would recommend replanting with a good soil mix of high humus acidic soil. Don't fertilize after the spring since that causes other problems.

"My question is, would it help or hinder my rhodos if I started using a richer media as a mulch? I'm thinking composted cow manure, which I have a lot of. Is damage from overfeeding likely with rhodos? I have no experience with aluminum sulfate, but would topdressing with this help with the pH issue that I think is likely?"

Several really bad ideas. Don't use cow manure or other manure as mulch. Aluminum sulfate kills rhododendrons and azaleas. It is good for hydrangeas but kills most other plants if used repeatedly. Powdered sulfur is the best for lowering the pH and it lasts.

"I also am wondering about using a foliar spray containing iron and/or magnesium to help them green up. Is that a good idea, do you think?"

The chelated iron foliar sprays will make it look better, but you need to fix he soil.

"Please help me. I know I goofed by planting these here, but the funny thing is, they ALMOST do well in this location. If only the baby shade trees planted in the front yard in front of the rhodos would hurry up and grow...cart before the horse, I'm afraid."

English Roseum will take full sun, but planted in sand is a real challenge. It doesn't hold nutrients or moisture. Replant using a good soil mix. Rhododendron have shallow roots, so be carefull to get a nice large root ball, but remove the lower part and replace with good soil.

Here is a link that might be useful: How to care for rhododendrons and azaleas.