the stock HU doesn't put out hardly any power - so new door speakers would help somewhat but not much - you really need a better HU (powerwise). or perhaps get a small 2-channel amp to power the doors speakers.
then power the sub with your rockford as you mentioned.
i have a similar setup (JL sub in custom box in the trunk w/a memphis amp) and JL components in the doors w/a JL 4channel amp pushing those...i am pleased with the way that it sounds.
if you want i could post some pics of the sub box - it goes in the "hole" in the S trunk.
in any case - i think that keeping the stock HU is a mistake - unless you aren't concerned with sound clarity. the stock HU in my '04 sucked!!!
good luck!