Thanks @Aizatulin for your input! Your solution is very elegant and provides clean results. I think the only problem for me would be, that the curves I use as input are based on real world data and often can't be smoothed that much without diverging too much from the original data.
Also I I'm not dead set on using the PathDeformer at all. My previous experience in modelling is in Cinema4D and I basically just tried to recreate the solution we used previously for this - but of course it has the same underlying problems in Houdini.
After sleeping on it for a night I now tried a completely different approach which delivers quite good results so far.
I basically take the outline of the curb, sweep it inwards for a small increment (50cm e.g.), then check for intersecting geometry with raycasts, fuse the intersecting points, then taking the new inside edges of the geo, convert it to a new curve, and repeat the process. It yields good results, there are just some stretched UVs here and there, but I think I can live with that! And I think with a bit more tweaking I could even get rid of those somehow.
This was a great learning experience, as it's the first time I feel I've used Houdini "properly".