Give the plates a good rinse with denatured alcohol before the final buff, that’ll go a long way towards getting the other stuff off. What colour are you sensitizing to? I like the second yellow myself. You are getting an image, so that is something!
The sun will give you faster results, but it can get just as hot as a lamp. I use a 500 watt light 10 inches above the plate with a squirrel cage fan blowing directly on the amberlith. It takes between 45 minutes and 6 hours to bring the image out for me. If you are guilding the image I would stop doing it at this point, it will serve no use until you get better images.
These look like they might of cooked, so your too hoe theory is valid.
Keep up the good work! you are almost there and the next 5 or so trys you’ll have it. One more bit of advice, if you don’t mind is only change one thing at a time. If you think it is the Methyl Hydrate, then change that and leave everything else alone, if you think it is the heat then cool the plate better. If you change more than one thing, you may not know which it was that was fouling the plate. This process takes longer, but you’ll learn more. (this is from the American Handbook of the Daguerreotype)