Firmware shouldn’t really make much difference to reading, it’s mainly to support newer media/include improved write strategies etc. Although being up to date never does any harm
Only things I can think of, would be to give the problem discs a real good clean, or to maybe try a lens cleaner on the drive.
But personally, I wouldn’t bother with cleaning the lens since it’s just selected discs, sounds like your drive just doesn’t get on with those particular discs.
Of course, an option for the future - should your NEC get stuck on more discs - might be to grab a drive that’s a more tolerant reader (such as a LiteOn or Samsung drive), to sit alongside your NEC.