Jeff Ascough warns that the most important first step is getting color balance right. Otherwise, your tone-mapping will be unnatural looking.
In playing with these various methods, I realized that some allow you more control and some less. Of course, too much rope and you might hang yourself. Be careful. In the final analysis, however, it seems that it comes back to personal artistic preference. Squeeze the tube from the end or from the middle. Whatever you like. (Unless you live with me. Then it has to be the end.)
The following examples were created using pretty strict adherence to the instructions here: The Digital Photography School.
Lab Color Method
This technique involves converting to lab color, copying the luminance channel, converting back to RGB and then pasting the luminance channel into each of the R,G and B channels. This retains a pretty natural feel which I like. Overall contrast needs a boost but that would be easy to add.
This method actually gives you a lot of fine-grained control because it allows you to tweak the hues in the image but, as you can see, it enables you to over-process and get an unnatural and flat look. There are bits of this I like and bits I don't. Maybe this would be a good type of layer to add for masking in the good bits. Not sure.
Here one simply creates a gradient layer in PS and then adjusts the gradient sliders. I like this method, too. It is easy. It results in a very natural look and it lets you quickly adjust black level, white level, midpoint and overall contrast. I think the tone mapping is just a straight luminance channel conversion to gray, however.
Channel Mix 72-28-10
This technique lets you blend the R,G and B channels separately. I used 72%, 28%, 10% for this image. In theory, I like this approach. In practice, I couldn't get a happy result. I added a softlight overlay to pump contrast a smidge and still wasn't happy. I think it is because the eyes lost their sparkle. That could be fixed with dodge/burn but, hey, what can't!?
One last comment (for now). I subscribe to Kathleen Connally's philosophy. Don't boil all the flavor out of it (my liberal paraphrase). It's easy to over-work an image. Be gentle. That's why I called it tweaking ... small adjustments.
More to come. Till then ...
PS - thanks to MJ for posing so perfectly still for all of these pics!