I use luminosity masks alot, but they have a different purpose to what dodge and burn achieves. Luminosity masks are based on actual image content so are limited to darkening or lightening the tones that are already present in your image. Dodge and Burn is used to alter image content independently, anywhere from a pixel to pixel basis going upto larger areas of your image. At a pixel level this is used to smoothen out the tone of an area without loosing image detail, and image detail could be anything from skin on a person to carpet on a floor.
If all you want to do is lighten an area and target a specific tonal range then luminosity masks are where its at, but most often their focus is to wide for detailed work and you will only alter what already exists within your image.
Dodge and burn is more about creating shadows where there weren't originally shadows, smoothening the transition or roll off from a midtone into a shadow or highlight, creating a light to dark transition where previously it may have all been a midtone.
Using the technique of an adjustment layer set to Screen/Multiply I rarely notice changes in colour and saturation, only if a major change is made it becomes obvious to the eye on screen. I always start my workflow with clean up and dodge and burn, after this I go onto colour correction which often involves very localized recolouring of image content to smoothen out colour tones and control hues. If there are major colour shifts this part of my workflow takes care of it, otherwise I can use the mask created when dodging and burning to target those colour shifts.
I use the same methods for dodging/burning as you, curves adjustment layers set to screen or multiply, and it works great. What I'm describing is just a way to do that same dodging and burning, but to do it through the filter of a luminosity mask. The luminosity mask simply excludes certain tones from being affected by your edits, but otherwise everything remains the same.
You can use it in conjunction with a screen or multiply adjustment layer, or actually make adjustments in the curves, or even other blending modes and other types of adjustment layers. By placing the adjustment layer with a luminosity mask into a layer group with a mask on it, you can "paint in" the areas like traditional dodging/burning by painting on the Layer Group mask.
I've found that it allows me one additional layer of control that I wouldn't otherwise have. The Luminosity mask narrows the tonal range I want to adjust, the layer group mask allows me to brush in the specific area that I want to affect. Obviously if you don't have a specific need to focus on a certain tonal range for your chosen image, there's no need to add a luminosity mask to the process.
I've attached an image showing what the layer grouping looks like in use...
Another cool variation on dodging that I've seen is to use the 50% Gray (or empty) layer set to overlay mode, but to then use colored paint instead of white/black for dodging. Just use the eyedropper tool to sample the color of your subject in the area that you're going to dodge, then increase the brightness of that color a little bit, then paint on your dodging layer. This seems to work best with dodging, and I've really only used it on landscape images. Just another thing to toss in the bag of tricks.