Before you starting playing around with pre softening (which doesn't work as lotions are acidic they close the cuticle), look at some white coverage rules.
Is the hair clean and free from oils (washed within 24-48 hours)?
Analysis the hair- double bases are for resistant hair - shiny coarse wirey hair that is harder to colour! Nothing to do with being 100% ( colour isn't that cleaver that it can figure out how much white hair a client has).
Have you picked exactly the right shade? Anything lighter with look like it hasn't covered.
Mix exactly 1:1 (using scales is most accurate)
Use the correct lotion- not generic.
Use plenty of product, placed onto the scalp with no overlapping - if you can still see scalp you haven't applied enough.
Heat will help to open the cuticle, and as wella said you can increase development time if needed.
We all know every major brand cover white hair otherwise they wouldn't make it. Pre softening, adding extra colour, and making stuff up can have an adverse effect on the hair and scalp, even something as simple as working on clean hair can solves your issues.