Part of the problem is the palette. FF1 used the first color for black, while FF3 used brown, green, etc. The first color in any palette will be the same on every palette. It's not the game or the engine, it's an NES limitation of some kind. If you were to re-palette the tiles (yy-CHR makes this really easy), then you should be able to more-easily convert the tileset over to FF1.
This is a screenie of an FF1 hack I started back in 2005 with my roommate. We ended up redoing the palettes to work with the tileset, which turned out pretty well.
Also, while we're at it, tiles aren't going to be necessarily assembled like how they are here. If you go into Hackster's Tile editor (double click on a tile), it'll look something like this:
That's how the tiles look in the rom, if you were to look with yy-CHR, Tile Molestor, etc. You do have some freedom to reassemble tiles here, but just be careful not to do too much too quickly. You may end up breaking a lot of tiles graphically in the process.