It's a shame Blender doesn't directly have an 'Offset Even' tool, along the perpendiculars to the edges being offset. A 2D curve can do it, so you could start with the trim, and build the plate away from it.. but starting with the plate as a mesh...
.. the E 'Even' option in the GG edge-slide tool means 'even along the crossing edge-rings', not a perpendicularly even distance from the loop itself. The illustration shows a sort of worst-case, with all the crossing edges vertical, so their density changes across the width. A simple GG (above) doesn't work.
If you're building the trim outwards from the plate, you could:
- Extrude the edges to be trimmed towards the center of curvature of the plate, like the rim of a Solidify modifier..
- AltE Extrude the new rim faces outward along their normals
- Delete the surplus faces.
This method. though, builds the trim inwards.
- As in 1. above, extrude the curve to be trimmed (top, in the picture below). This extrusion won't do anything except to tell the next operator what to do..
- .. Which is I inset the region of all the faces in the original plate, with 'Even' checked, no 'Edge Rail', and no 'Boundary' inset. (Bottom, above).
- The extruded faces have done their job, helping a selective inset, and can be deleted.
- The new border-strip of faces can now be AltE extruded along its normals.
(I've had to tidy up the inside of the plate a bit, reconnecting the top and bottom with Bridge Edge Loops .. the topology inside your plate looks better than this, from what I can see)
Add a Bevel by angle modifier, and a Subdivision Surface..
The edge-lengths do check out.. they're pretty much the same all the way along the trim.