I have NO idea what I'm doing, and would really appreciate a really broken down, idiot's, step-by-teeny-tiny-step guide to fine tuning the map once you've aligned it with the align tool.
By your description, I believe you've stretched the map cells not to the same size of the grid cells but to a common multiple: Imagine the playing grid is 60 pixels wide, that the map grid is 59 pixels wide and that your map has 120 cells. With only one pixel difference, the first cells seems perfect. But the funny thing is that the last cell fits too, because the last map cell goes from 7021 to 7080 and the last grid cell goes from 7020 to 7080. However, after 30 cells, a map cell goes from 1770 to 1829 and, at that location, the grid cell goes from 1800 to 1860. They are completely wrong! The reason for that is that you've got 120 map cells but only 118 grid cells. The solution is to stretch the map the entire width of two grid cells and try again. So do a "Set Dimension", make the map 120 pixels longer and try again. Now, each map cell will have a new width of Width+(Total_Stretch / Number_of_Cells), or 59+(120/120) = 60, which is the grid width. pro tip: You can try at random until it fits, but the way to know exactly how many cells you need to stretch or contract, is to scroll to see how many times the cells get out of phase. i.e.: In the example above, the cells fit at 1, 60 and 120. They don't fit at 30 and 90. Two points of out of phase means you need to stretch or contract the map the width of two grid cells (120 pixels).