Best way to bevel extruded curves?

Question

I'm trying to bring our company logo into Blender to create a 3D model of a plastic part, for a concept visualization. I can import the SVG just fine, and extrude it in the Curve/Geometry properties. However, when I try to add a bevel, the geometry inflates so that the bevel is outside of the original curve, not subtracting from the extruded solid like a bevel should:

Since this is a logo, this won't fly, especially as the rest of the design has some quite narrow gaps which get closed up by this bevel behaviour.

I have also tried converting the curves to meshes, but these are so poorly tessellated that there's no way to bevel them in edit mode or with the modifier.

Any suggestions?

Use a negative Offset value on the curve matching -1 x Bevel Radius — Duarte Farrajota Ramos, May 11 '23 at 20:45
I've looked for a bevel offset control, but I can't find it. Where is it? — Dan Bennett, May 11 '23 at 21:02
Ah - I see what you meant. That works, but there are artefacts where the geometry now overlaps. — Dan Bennett, May 11 '23 at 21:05
These artifacts are still visible when rendered in Cycles. Small black patches. — Dan Bennett, May 11 '23 at 21:06
Yes, hat is a well known limitations, no elegant solution other than converting to mesh and manually fixing it. See https://blender.stackexchange.com/questions/51327/bevelling-concave-curve-part-results-in-buggy-mesh/ https://blender.stackexchange.com/questions/92632/creating-an-bevel-inset-on-an-imported-svg/ — Duarte Farrajota Ramos, May 11 '23 at 21:15
Yes, that's what I'm trying to do now. It's not easy, and I'll have a lot of vector shapes to fix! — Dan Bennett, May 11 '23 at 21:23

Best way to bevel extruded curves?

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