I got inspired by your post and I ordered a SOLARA 19" LED TV; 125EUR P&P included.
Just did some testing. CVBS input from A1200 does not give a high quality output but I did find a DB23->SCART cable and that gives good de-interlaced output + sound. See attached picture. VGA output from the scan doubled A3000 output or CV64/3D on a A4000 also works perfect. Did not test the HDMI input yet but none-the-less incredible what one can get at this moment for less than an Indivision. The TV should even allow playing music and videos from an USB stick.
Sure, the screen is rather small but nothing worse than the 1084S it is replacing.
I moved around a year ago (you can see that the F7 did not survive the move). I just get to being settled to start some hard work again (development etc) but I now just had a session of Slamtilt. Switching to the hires screen in that game still gives a rock-solid picture. I blame you for my lost productivity 
Sell the 1084s. Not everyone is happy with the output of el-cheapo lcd's (especially with fast moving images)