Thanks Ashley, that solves the tile border issue. Unfortunately though now I can't apply the distortion effects I want (noise, bulge, blur, glow...) to the low quality render without it looking really bad.
I'm not sure if I'm doing this correctly (applying effects to a white tiled background on the top layer which multplies everything below it), or what I want is just not possible in C3.
The way I would do this in SDL2/OpenGL would be to render everything to a texture at the base resolution and then upscale the texture to the screen/window using bilinear filtering and apply the shaders/distortions to that.
The only way I've been able to achieve the effects I want without tilemap border issues in C3 is just to not use tilemaps and use sprites/tiled backgrounds for common platform patterns instead, but obviously this means buildings levels is more time consuming, and probably runs slower.