Getting an object to bulge/bow

I’m a noob so any insight would be helpful. I import an svg of a logo into Blender, extrude it, then turn it into a mesh from a curve.

The image is a poor representation of what I’m trying to accomplish, which is taking the logo and making it bulge and round out. The 2D is a top view. Then there’s an ortho view right side and view from front

I’ve tried using the curve modifier around a circle and using the screw modifier. Also the warp modifier. All with no success. The meshes are triangles which really mess the modifiers up so I remesh them to get quads but the more detail the object to more taxing it is on the PC to create the quads. I’m just not sure it should be that hard.

Crappy mesh = crappy result whatever you do.
If the triangular mesh is not giving any good results when bended you first need to fix this underlying problem, don’t be lazy, you’ll just be taking even more time later on overcoming basic problems. Retopologise your mesh or manually convert triangles to quads. The remesh modifier is not for retopologising a model for such a situation as this. There are many tutorials about retopologising, juse search for them
To give this bulging effect you can use a lattice modifier

more then one way to do it

I would first make the 3D shape
may be using nurbs surface to get something smooth
then use the knife project to get the 2D pattern on it !

did a quick model here

do some workings line in 3D to defined min max
then add a nurbs surface to do 1/2 of model which is symmetrical in this case
mirror is your friend here

happy bl

Thank you. I wasn’t trying to be lazy. Just couldn’t think of the right terms to search for. I appreciate the help.