I'm not entirely convinced that your trickery of scaling battle tiles down from 20x20 to 19x19 at 1080p works. When I was just scanning the article, seeing how long it was and looking at the images, I was able to notice immediately that something was off. I'm going to do my own short analysis of a small section of the screen(using this as the base area of the screen to look at)
Due to the way new accounts are limited on the number of links they can make in a comment, I've put a Pastebin with the numbers and their corresponding links here: http://pastebin.com/j6JGZyeP
ADMIN: great feedback! I edited your post to put the images inline, and upgraded your permissions to level 2, "member."
Firstly, the dark tiles and water tiles look mostly fine. I don't see any glaring issues with the dark tiles, but the water tiles have some obvious scaling issues near the bottom/top of each tile but this is an OK scaling issue for the most part. It sucks, but without proper 2x scaling, it's mostly fine. Those two tile types are OK. Not shown in the picture, but the sand tiles look fine too, about on par with how the black tiles scaled.
However, there are two glaring issues with the area.
Firstly, the rocks in the water. I'm blowing this way up so you can see the scaling issues without being constricted by the few number of pixels(base image here, blown up image here. none of those images are perfectly square but the pixels didn't get further distorted in the scaling process so it's fine). The rocks just look so off. The parts that scaled down on this sprite make it look so much worse. For example, here, there's a rock that turns into a long horizontal line due to where the scaling fell. Upon taking a closer look, there's an obvious grid all over the image, which I've drawn (not perfectly straight) lines on here. After noticing it on this tile, I can't not notice it everywhere.
But then the grass tiles are the worst offenders. Not only is there a grid, it's noticeable due to where it fell. This is what told me the scaling was off when I was scanning the article. This time, I've just circled the line where it occurs here. On that whole vertical stretch, there's an obvious line because the dark green just highlights it against the base green that the grass is colored. To be fair, this visible line did exist slightly in the original art, but with the scaling falling on that exact line, it just highlights it even more and makes it painful to look at.
I don't really have anything else to say about this. I really love the pixel art of the first game, even if I can't look at it up close while I play. If the HD remake has the option and finds a different way to scale things up, I'll definitely use the original art instead, but at this point it's looking like the higher res art will be the way to go for me, personally.