I thought you might wait until the home management system was distracted by other interests and make use of the ordinary oven, Blumbly, for a test run on one or two heads. If it works, and you are still on your feet, you could consider procuring a surplus electric convection oven from a thrift store or flea market.
Chemical cleaning can be done but tends to eat the aluminium, leaving a rougher surface than you start with. The highly effective chemical products are also highly dangerous, requiring full protective clothing - and realistically, could never be used legally in industry outside a sealed protective cabinet. Here is what may be the most effective of them:
http://www.enertechlabs.com/Power_Clean_Acid_2033.phpNote that stuff is a mixture of hydrofluoric, phosphoric, and sulfuric acids with some surfactants (wetting agents). Hydrofluoric acid is a substance that makes chemists turn pale at the thought of using it (I may be exaggerating, but only slightly).
There are slightly less hazardous products that omit the hydrofluoric but still have phosphoric and sulfuric with surfactants:
http://www.jmnspecialties.com/list/jmn-products/general-cleaning/10-aluminum-cleaners-acid.htmlMore realistically, you might experiment with some more ordinary chemicals - hydrogen peroxide can remove stains from aluminium, but is still a hazardous material and won't cut through crud, just stains.
Generally, Blumbly, as far as I can make out, the people who use the extremely dangerous stuff like Powerclean are small businesses doing jobs like cleaning aluminium trailers and road-wheels, perhaps in disregard of both the law and ordinary social responsibility. Splash that stuff and you'll not only be blind, you'll look like a fully made-up actor in a zombie movie.