Your 1st step is wrong, as the initial raster is in EPSG:4326 it should be:
gdal_translate -a_srs EPSG:4326 -a_ullr -104.7 30.8 -103.8 29.8 MRMS_RALA_LATEST.tiff projected.tiff
Then your 2nd step will correctly reproject the raster to epsg:3857 for web mercator.
gdal_translate needs the coordinates of the corners - I don't know where your " 729000 528000" come from - I guess the width/height? No, it should be the coordinates:
gdal_translate -a_srs "+proj=gnom +lat_0=50.008 +lon_0=14.447" -a_ullr -301500 +217500 427500 -310500 QQNDR.png located.tiff
Another change I've made is to name the output .tiff since its a ...
Thank you very much for posting your workflow, this helped me with a similar issue I was having. In case this might be useful to somebody else, I used different python functions for my raster mosaic. In my case, the no data value for the VRT was 255 and because my data only goes from 0 to 100, I masked all the values in my VRTs greater than 100 before ...
There's a QGIS tutorial "Wildfire Monitoring Using The Semi-Automatic Classification Plugin" that seems to cover downloading as well as the necessary analysis steps. I haven't tried it myself but it should be a starting point.