There should be no problem with using the HU amp to power the factory speakers by bypassing the factory amp, even though the ohm load is different for the front speakers than the rear speakers. The difference is the sound level will be different front to rear, which can be adjusted using the fader. Is this correct?

That's correct. May be different depending on the efficiency of the speakers front to back. Will not cause a problem with the HU. Use a AA battery to buzz out the speakers making sure you don't have common ground. Each speaker should have two separate wires going to it. You must have "four" wires going to say the rear; not "three" wires. Three wires going to two speakers is called common ground since they have to share one of the wires. Thus that wire is common to both speakers. Your HU will not like that situation. If that situation exist you have to run new speaker wires or one wire to make it "four" two to each speaker. BTW buzz mean holding one of the pair of speaker wire to the bottom of the AA battery and using the other to touch the top of the battery a bussing sound will be emitted from that speaker. This tell you that good connection exist to that speaker. Do this to all four and you will be in good shape.