This problem may occur both in traditional printing and scanning, but most scanners do not perform well with dens and high contrast negatives. These Images are scanned, but if I would digitize them today I would use my Nikon camera instead. Shooting the negative gives more options regarding the exposure.
I found that one advantage of using old film is that it tends to be less contrast. The exposure also has some impact on the contrast. Normally a small to large overexposure is advisable, but testing different exposure to find the right look is a good course of action.
If you develop the film by your self, experimenting with the development time can be a good advice.