The green tinge is strange, unless your original is an RGB file rather than greyscale. Not much value in keeping that way if it is and it will remove your colour cast.
Today with digital tools, I find straight dodging and burning to be a little primative. Its merely darkening or lightening an area. What I find significanly more effective (and scanned B&W film is all I really do) is, in photoshop, make adjustments via the curves while only looking at the effect on the area in question - ignore how it affects the rest. Then mark that as a "History State", go back to the state prior to applying the curve, then with a 20%-ish transparency setting, use the "History Brush" to paint that effect in where you want it. Same application as dodging and burning yet it allows you much more control over how you work areas...
As Im 100% film, Lightroom for me is merely a database...
Leica M's + Mamiya 7II