gdal - gdal_translate Bilinear Interpolation

I am working with the v2.3.3 NuGet of GDAL by Tamas Szekeres for the .NET environment, and can successfully open the etopo1_ice_g_f4.flt raster to cut basic tiles.

The problem I am having is that even when I apply the -r bilinear option to my translation options, the generated image remains pixelated.

Specifically, I make the following calls in code to get the initial raster (simplifying the file names for this example):

GdalConfiguration.ConfigureGdal();

var etopoPath = @"F:\testing\etopo1_ice_g_f4.flt";
var colorPath = @"F:\testing\color.txt";
var pngPath = @"F:\testing\tile.png";
var tifPath = @"F:\testing\tile.tif";


var raster = Gdal.Open(etopoPath, Access.GA_ReadOnly);

I then set the appropriate projection extents, which will produce a 256x256 tile (in OpenMaps, it would be tile x = 306, tile y = 389, zoom = 10):

// shows us tile 306 389 z10
const double lonWest = -72.42;
const double lonEast = -72.02;
const double latNorth = 39.64;
const double latSouth = 39.24;

I set up the gdal_translate options to include bilinear interpolation:

var translateOptions = new[] {
    "-of", "GTiff",
    "-projwin", $"{lonWest}", $"{latNorth}", $"{lonEast}", $"{latSouth}",
    "-outsize", "256 256",
    "-r", "bilinear",
    "-q"
};

Gdal.wrapper_GDALTranslate(tifPath, raster, new GDALTranslateOptions(translateOptions), null, null);

And finally, process the GeoTIFF as a color-relief tile:

var demOptions = new[] {
    "-of", "PNG",
    "-q"
};

var tifRaster = Gdal.Open(tifPath, Access.GA_ReadOnly);
Gdal.wrapper_GDALDEMProcessing(pngPath, tifRaster, "color-relief", colorPath, new GDALDEMProcessingOptions(demOptions), null, null);

And it works, producing the following PNG image:

Now, the problem is that this does not seem to have been interpolated. The same image is produced even when -r bilinear is removed from the options.

Using the same elevation data (etopo1), and doing my own bilinear interpolation processing, I get this image:

I would like to not have to get the raw elevation data and do my own bilinear interpolation... I'd rather have the image properly interpolated coming out of gdal_translate.

So, am I missing something?