You could make this work if you do it VERY carefully. It would probably be MUCH easier to build the coaster first, then create the holes around it, than to try to build a coaster to fit pre-existing holes.
AFAIK, every coast and even the steam trains will fit through a 4m vertical opening. And except for some of the really wide wing coasters, all of them and even the steam trains will fit through a 4m horizontal opening. HOWEVER, you can only get them through holes this small if the track is perfectly straight and either perfectly level or (in your case) perfectly vertical for some distance on either side before and after the hole. Otherwise, it won't fit. Also, for the 4m width, the track has to centered relative to 1 side of the opening, and as close to it as possible for the height.
So, what I would do is this: 1st pick a coaster you know will fit through a 4m-wide opening and can have perfectly vertical track. Build the coaster with autotunnel on so you can dive it straight down some ways underground. Then pull it up however gradually you need due to the speed, until it's going vertically back up and gets back above the surface. Go on and complete the rest of the track. Having done this, go to the holes and build the walls around the track using very careful placement via advanced move. Once you have the walls built, then level the ground to the top edges of the walls, and finally make the path around the holes, using the grid of the walls already in place.