You could use HDR (high Dynamic Range) processing. It’ll take longer, but do at least two RAW mode (.dng, not .jpg) images (3 would be best) while parked at a dead stop above each photo point. Make one shot with a shorter exposure set for the sunlit areas and a longer exposure one for the shaded areas. Personally, I would even do one more with full area matrix exposure. That way, you brighten up the shadows more by keeping the exposure set correctly for them, and properly exposing for the well lit areas in the same final image.
Do not to change exposures between all the photos in each set though, find what the best exposure is over a well lit area and use that for all of your first set of bright area shots, and then also check for the best exposure over a very dark area and use that for all of the second set of dark area shots. Also, be sure you’re just adjusting the exposure setting for both sets of photos using shutter speed only and the aperture is locked. Funny things happen, like different levels of depth of field, between images when you change aperture.
Several processing programs, including Photoshop can work with HDR imagery to blend them together into one uniformally exposed image.