1366x768 is not a great resolution... It's too high for 1 x, but too low for 2 x. I 1920x1080 is much better as you can have PAL x 2 and have 540 lines, which is 512 plus an amount of overscan that the Amiga can easily handle. I've had some success with 960x540 that fills up the entire screen, but I now mostly use 720x540 with black bars on the side.
I guess with 1366x768 I'd try setting that up for 2 x for the Workbench so that would be 683x384, a bit low but workable. Or tweak 1024x768 to show the correct black bars with no stretching. I've got that working for 720x540x2 = 1440x1080 so it should also be possible for 1024x768. Then perhaps set the overscan to a lower resolution to allow for more chip RAM access for the CPU. But for any PAL or NTSC games I don't see any way around a non-integer resolution.