1. Take a blank, properly aligned grid cell and exactly fill it with landfill. I use the ChunkyChunks mod for custom gridlines to make this easy.
Step 1
2. Build or copy your blueprint in the landfill cell, aligned how you want it to be aligned within the cell.
Step 2
3. Use the blueprint tool and grab an area at least containing the full grid cell. It doesn't have to be exact at all, as long as you don't grab any entities/tiles outside the cell.4. Finally, under "Filters", check the "Tiles" option, then check "Snap to grid", then uncheck "Tiles" (unless you want the landfill in the blueprint). It's important to do it in this order. We want the landfill on when we enable "Snap to grid" so that it will use it for grid size + alignment. You should have a perfectly grid aligned blueprint. Easy!
Step 4
This technique is even helpful if your blueprint extends outside of the grid cell. In that case you still need to do some manual work to set the grid size and alignment, but you can use the landfill tiles to align the grid border.