@start81,
The company we were expecting from Nicaragua arrived two days early, so I only had about an hour to check on the Amiga for you. Turns out the HD is flaky, so I couldn't really look at the settings for you.
But! Very good news -- I found some of the things that had helped me get it working in the first place. Other people had similar problems getting LCDs to work with graphics cards. It wasn't just a Picasso II and Sony monitor problem. The solution was to get the horizontal frequency close to 60Khz and make sure the vertical frequency was within your monitor's range.
Using Picasso96Mode, duplicate one of the screen modes you would like to use (say 1024x768 at 256 colors). Edit this duplicated settings file. The important parts are CLOCK and FRAMESIZE. The horizontal frequency is the pixel clock divided by the horizontal framesize. The vertical frequency is the horizontal frequency divided by the vertical framesize. If you are already seeing about 60Khz for the horizontal frequency, then it's the vertical frequency we need to try to lower. Lowering the CLOCK should do the trick. Adjust it and try the TEST button and see if it works. If it does, save it and use it. For example, if that 1024x768 mode has a clock of 80MHZ, a horizontal frame of 1304, and a vertical frame of 815, then the horizontal frequency is 61kHZ and the vertical frequency is 75Hz. Changing the clock to 68Mhz will reduce the horizontal frequency to about 52Khz and the vertical frequency to about 63Hz.
I remember having to play around with it like this to get it to work. I don't think had I gotten my Amiga working today it would have helped much since I'm using a Cybervision64 (4MB) on an A3000. Different hardware might mean different values.
I hope this helps, or at least points you in the right direction. Come to think about it, I had to set similar parameters when I was installing Linux on one of the Pentium boxes to use that monitor, too.
Here's a link to working with Picasso96Mode:
Link-David