The ag handbooks make clear in their various tables that the max/min tire pressures quoted for various sizes are usually based on a maximum speed of 25 mph road speed for farm tractors. At that high speed considerable pressure is needed to prevent unnecessary sidewall flexing and to bear sudden vertical axle loads.
Yet, the manufacturers also give footnotes for operations at 5mph - 10 mph or lower, saying that the load bearing capacity of the tire is up to 80% higher at low speeds, such that lower tire pressures can be used.
Since the 3038e has a maximum speed of nearly 15 mph, Deere must cite minimum tire pressures than can bear axle loads at that speed. This is why I take the 12 psi minimum pressures in the rears as just a guide. R4 industrial tables usually show R4s to have tremendous load bearing capacity--in my case, the load bearing of just one rear R4 is more than the weight of the whole tractor at standard recommended inflation pressures!
I dont want to get any one in trouble here, so proceed cautiously. Keep in mind that if you lower your tire pressures below the recommended (all speed) minima, you must check tire pressures fastidiously as air temperature falls, otherwise you could get into some trouble, particularly in the smaller front tires.
See the two links below, the first being an excellent University of Kentucky summary, the second being the full Michelin Ag Handbook. Look at the wide range of acceptable pressures in the U of K example, down to 6 psi. Note also the warning to lower your pressures as much as is consistent with supporting the axle load.
http://www.ca.uky.edu/agc/pubs/aen/aen93/aen93.pdf
See pages 12 - 13 for compact tractor R1 specs at low speed in the Michelin Ag handbook:
http://www.michelinag.com/agx/en-US/products/product_detail_pages/09Michelin AG_DataBook.pdf
Hope this helps.
Tim