I've spent for too much time & money any man should have to spend on displays and have learned the following...
There are problems with using lcd's for Amiga scan doubled displays. Heck.. trying this with big box Amigas fitted with a graphics card like the retina or CV64 can be a hassle.
Why? your video output must match the LCD monitors "optimum" resolution. Anything else is a comprimised solution with some undesireable artifacts...
For instance, I have a Dell 19" that runs at 1280 X 1024 optimum resolution. If I try to run any lower resolutions from my PC's graphics card I get a blocky pixelated effect or soft edges. Sure this montior handles this problem beter than most... but I want a sharp LCD display dammit!
The same thing happens with my Macbooks display to anything lower than the recommended resolution. Soft hazy edges or unwated pixel artifacts...
However a CRT VGA monitor connected to an Amiga (with a scanboulber or flicker fixer) handles any Amiga res scan doubled screen just fine, no soft edges, or blockiness.
So if it's a matter of having one display for all your consoles and PC's, I'd go for the LCD route and live with the blockiness.
I deal with this.. I have my Xbox1, PLaystaton2, Dreamcast, Amiga, Xbox360 and PS3 connected to a Hanns G 22" montior. I route the consoles through a component switchbox, and the VGA through another switchbox.
Of all the systems the XBOX HD games,Xbox360,and PS3 look the best because they can do the native 1080i/P that this montor dislays. The dreamccast, Amiga and ps2 look "jaggy or pixelated"
With all that said the best Amiga montior I have was the Toshiba Timm, 20" crt TV, RGB, and VGA. It did 15.75 Klhz. I had 2 of them and recently sold off the last one.
The Hanns-G is the closest I've found in price point and versatility.
If I could do it all over again, I'd find a modern display that can swith ascpect rations from 4:3 and 16:9, and display the Amigs native 15.75 klhz video. I've had the scan doublers but they're so expensive I just sold them off...
So if you're willing to invest the time you can find a montior capable of handling all your needs. One guy on Ebay sold an Amiga 1200 bundle with an HD lcd monitor capable of doing both VGA and Amiga 15.75 klhz RGB.
Make sure you can return the monitor for a full refund.
Sorry for the long post but I've been though this dilema, trying to help...