Through testing, there are three ways:
-Using Grid warp and making the longitude/latitude lines perfectly straight. Only works if projection has perfectly straight meridians too.
Reason is that Grid Warp only shows 1 layer instead of the whole image, so I can't use the coasts to reference.
Example: https://drive.google.com/file/d/1bbrstNSZBG4TTmSt2Nt32lV8TfwsU4QP/view?usp=sharing
You can't see the background, which does have perfectly straight meridians.
-Using Distort This! plugin. Probably the most effective. Only shortfall is that there is a limit to how far you can pull the nubs.
-Making small sectors of the map and using the cropping tools to make the coasts line up, which is easier since area is smaller.
Edit: An example of Method 2 here.
