Disclosure this is an answer to my own question
Question 1. "Can the original 16bit elevation value be back-calculated (algebraically) from the 32bit RGBA values if the image is rendered using color ramps?"
Without processing the raster, I'm unsure, but my gut tells me it is possible although simple ramps do not seem sufficient.
Question 2. "How could the original image be converted into a 32-bit RGBA image (using R and G bands in QGIS for example), such that the original 16bit precision persists? How could the original elevation be back-calculated algebraically from the utilized bands?"
To do this using two bands is actually quite simple. Each 8bit band may contain a value from 0-255. Two bands of 8bit ==> one band of 16bit.
Deconstruct the 16bit raster
The built-in QGIS 3.4 raster calculator does not appear to have the functionality needed. GDAL(gdal_calc) has access to Numpy (Python library), and with it we can perform two raster calculations as follows:
From the 16bit elevation raster input we divide by 255. We also must truncate the fractional portion of the resulting number using trunc() in the expression. This value will be encoded to one band of an 32bit RGBA.
gdal_calc -calc "trunc(A/255)" -format GTiff -type Byte -A dem.tif -A_band 1 -outfile dem_div.tif
We calculate the second band using the modulo function on the same 16bit input raster, which returns the integer remainder of a division. This value will be encoded in a second band of the 32bit RGBA.
gdal_calc -calc "mod(A,255)" -format GTiff -type Byte -A dem.tif -A_band 1 -outfile dem_mod.tif
Construct the 32bit RGBA
Using GDAL or QGIS's merge raster command we assemble each 8 bit image into 2 different bands of an RGBA output raster.
Back-calculate from R & G bands
To back-calculate an original 16bit value we simply assemble the pieces with the JS or equivalent code:
(pixel[band0] * 255) + pixel[band1]
A few notes:
PNG is a lossless format and widely supported in web browsers, which makes this possible. This conversion will not hold true in a lossy format like JPEG, because the compression has changed the data.
Using raster data in GIS oriented web applications poses a real challenge primarily because of limited image format compatability. Newer webmap platforms are making improvements (Mapbox now allows for GeoTIFF), but limitations still exist in other systems. Consequently, it can be difficult to leverage the use of rasters as we would in primary GIS softwares.
This is a 16bit DEM rendered in greyscale
This is an equivalent 32bit RGBA DEM rendered in red and green