You might be surprised by how much you need to burn in to get any effect. Try test strips of the highlight areas only and over-shoot by at least one stop from base exposure, then say 1.5 then 2 stops etc Then you can narrow it down later. Assuming that 5-8 secs represents the best overall exposure for shadows and this is quite short even if it is only 5x7 prints, then another 8 secs is only one stop.
2-3 secs more based on how you describe the highlights is totally inadequate as you discovered
There are other things that you might do but initially I'd try what I have suggested first.