3d chess pieces from bezier curves I am trying to make a chess set in Blender

I have made chess pieces blueprints as 2d bezier curves in Adobe Illustrator. Now I would like to import them to Blender and then using Lathe-like operation create 3d shapes from them.

It appars that if I export/import SVG files, there's tonnes of problems, like wrong pivot point etc.

Is there a quick and easy way to make what I intend to do?
Thank you
Check this on changing the origin of the imported SVG curves: Change pivot or local origin of an object

I imported the SVG from Illustrator, changed the origin point and added a screw modifier. One thing to note, my imported SVG curve was a closed shape. I deleted a curve segment on the axis I wanted to spin around by selecting the two curve point that made the segment, right-clicked and chose "delete segment".

Here's a file you can see an example.