Earth engine - ee.Terrain.slope() output at wrong resolution after DEM mosaicking

The big picture: I’m using Google Earth Engine (Javascript) to do a terrain correction on Sentinel-1 imagery, as in Andreas Vollrath’s work. However, I want to use a higher-resolution Canadian digital elevation model, CDEM (see documentation here) instead of the SRTM DEM.

CDEM comes as an Image Collection rather than an image, so needs to be mosaicked into an image before being put into a larger terrain correction function, where I use function terrain.slope() to get the slope from the DEM. However, when I mosaic this dataset, terrain.slope() does not produce the slope output at the same high resolution of the CDEM dataset (though the values and data types look correct). However, if I do not use mosaic but call terrain.slope() on the mapped CDEM ImageCollection, it turns out correctly (but with no-data borders around individual images because of edge effects).

My questions: can I make a mosaic of the CDEM that I can use in the terrain.slope() function, and have an appropriately scaled slope layer as output that can be used for terrain correction? What part of the mosaicking process results in the lower resolution slope layer? Note that I’ve tried mosaicking by using mosaic() and a median reducer, and both lead to this problem.

You can view code that illustrates my problem here: https://code.earthengine.google.com/331ddb0c3324256ebd4ec1ea0db4402c

The section that is problematic is:

var dataset2 = ee.ImageCollection('NRCan/CDEM');
var elevation2 = dataset2.mosaic()   //somehow this line causes problems for the slope layer***
Map.addLayer(elevation2, elevationVis, "CDEM")  //as a DEM it shows up fine on the map

//calculate slope in radians
var alpha_sRad3 = ee.Terrain.slope(elevation2).select('slope')
            .multiply(Math.PI/180).setDefaultProjection(proj);
Map.addLayer(alpha_sRad3, {}, 'slope CDEM') //lower resolution than the elevation2 layer - why??***

Whereas, if you do the slope function on each individual image in the CDEM dataset, it works:

var alpha_sRad4 = dataset2.map(function(image){
  return ee.Terrain.slope(image).select('slope')
            .multiply(Math.PI/180).setDefaultProjection(proj);
  })
Map.addLayer(alpha_sRad4, {}, 'slope CDEM collection')

Note that 1) this problem also exists for terrain.aspect(), 2) I moved this question here from StackOverflow, and 3) the terrain correction is also discussed here: Terrain correction (flattening) of Sentinel 1 images

Thanks!!