@Rich Dersheimer:
Thats it, you have it exactly

And yeah, its not too much in the way of code; but extracting the relevent bits from the whole project would be a bit of a pain.
The curious thing about the problem I was having is that in several places in the original picture, the same tile is drawn correctly in one place, but incorrectly in another.
@Mobiius & @revenant chaos:
Apparantly using
set object filter worked the second time I tried it. I did try it last night when mobiius suggested it, but I think I put it before I textured the tiles and it didn't work.
So yeah, problem solved

by simply using
set object filter objNo,0
but
after the object had been textured.
Thanks to everyone who suggested stuff