> The slider runs along the whole trade-off between distance and climbing [...] Climbing is cumulative gain

Another mechanism might be a kind of user-defined cost-curve, where a gradual climb to 10 might be preferred over a steep climb to 8, etc.

You want OpenTripPlanner. Their triangle lets the user trade distance, climbing, and safe facilities.

https://github.com/opentripplanner/OpenTripPlanner

https://github.com/opentripplanner/OpenTripPlanner/blob/dev-...

Or brouter with custom weights also has a lot of tuning points