it wants everything to be in the one resolution the monitor wants.
I strongly doubt this. If this was true, you wouldn't be able to enter the BIOS of a PC or install Windows on it.
I rather think it has a discrete set of resolutions it supports. I am quite sure that 640x400, 640x480, 800x600 and 1024x768 are among them.
Another problem could be the repeating frequency. While on CRTs you tend to use high frequencies like 90Hz or higher, most TFTs work best with 60Hz and might not accept anything above 75Hz.
In either case what you have to do is to check the monitor's manual for the supported modes and frequencies and use the Picasso96Mode program on the Amiga to adjust your screenmodes to these frequencies.