Applying text curves to a non planar surface

How can I take text curves and have them applied to a surface like they would in real life. Projection and/or extruding/trim will distort the curves depending on what there angle of the surface is correct?

I am trying flow along surface. However can’t get a basic test of this to work.
First issue is that when I am using a surface that has been split from a larger surface it wants to use the overall larger surface. I have to recreate the surface using a loft after duplicating the border.
Second issue the UV’s i’m having adjusting to work properly on a simple test.
Once I get this in the right direction is it going to distort the curves if my base surface isn’t the exact dimensions?

Please tell me there is an easier way.FlowSurface Test.3dm (70.0 KB)

There are a couple things messing up FlowAlongSrf.
1 - The curves surface does not have even parameterization like the original surface. Rebuild the curved surface to even it out. Then also Rebuild the flat surface to have the same points and degree.

2 - The two surfaces have UV directions swapped relative to each other. Use the DIR command on one to swap the UV directions.

Then FlowAlongSrf will work fine.