QGIS not displaying straight lines correctly in different projections

[DPKdebator]

Recently I've begun to mess around with QGIS for mapmaking, since it's a powerful program and is a useful tool despite the high learning curve. For my first QGIS map I am doing a greater United States map, which has been going mostly fine so far. However, I've run into a pretty big problem when changing the projection. I've been using the Mercator projection to draw straight lines, and will display the final product in a conic projection.

The first image is a Mercator projection, while the second is a US-centered conic projection. As you can see, some of the lines of latitude display perfectly fine, however many of the custom ones are not curving properly. Some of the custom lines are fine, like Nebraska's northern border:

Would anyone with more experience in QGIS be able to help me fix this issue?

 

[DPKdebator]

After looking into the problem some more, I believe I have figured out the problem. I noticed that some of the lines I had drawn on my own were only connected by two vertices, and this resulted in them not curving. I experimented with adding more vertices to the lines, which ended up fixing the issue. An easy way to add more vertices and ensure that both shapes have them in the same place (which avoids blank space from forming) is to use the Split Features tool and draw right triangles (enable advanced digitizing and set "a" to 45 degrees) across the line, then merge the original shape with the triangles that were created. Any shape of triangle probably works, but I just tried it out with right triangles to have roughly equidistant vertices.

To check the results, change the projection, and... voila!

 

[lock]

Yep. I had the same problems. And I had a slightly different solution. Zoom in fairly close and then use the arrows to move the map while double clicking without touching the track pad.

But I like your method too for lines that aren't N/S or E/W.

.