One solution is to use something like Amigamaniac's RGB to S-video adapter.
http://www.amigamaniac.com/RGB_to_PAL_NTSC_adapter.htmlThen just team it up with a LCD TV of your choice. Many of the less expensive models also support PAL as well NTSC. Usually its the higher end models (like Sony, toshiba, panasonic and etc) that don't support PAL at all. I have 2 Vizio HD sets, a 47 inch and 26 inch, that both work just fine with PAL signals.
His S-video adapter has an extremely good picture. Probably 90% or more of the picture quality of RGB. Very sharp and clean.
Depending on the LCD TV and how it handles interlaced and non interlaced video, you should be able to run your desktop in High Res Laced and possibly Super High Res. Something 1084 monitors certainly don't handle very well.
I currently have an RGB crt I use on my A1200, and this is the solution I am going to use going forward. Tired of limited and low res video on the Amiga when its capable of so much more.