Ok, update on my last two posts just above. After feeling pretty confident that they ordered the old dash part number, I called the dealer again. First talked to the service dept, who told me parts dept would not be able to order the wrong part number. They told me to call the parts dept to discuss why that part number was ordered. I hang up and call the parts dept and ask them to pull up the TSB. They pull that up, but also pull up a different document that lists warranty parts replacement (or something like that). This other document has more of the old part numbers and the corresponding new part numbers (04005-14935 for me). So then he said they would order 04005-14935-B1 and I say "NO NO NO, it should be 04005-14935-B0". He says "oh, you're right, B1 is the lighter color". So hopefully 04005-14935-B0 is on order.
So based on my research, I believe the following are the OLD > NEW part number combos:
(standard dash) 55401-35900 or 55401-35908 > 04005-14935
(premium audio) 55401-35901 or 55401-35909 > 04005-15135
-B0 is the darker gray (for dark gray or stone interior)
-B1 is lighter (for fawn interior)
Looking at the parts on the following Toyota parts website was helpful (scroll to Pad Sub-Assy, Instrument Panel Safety section):
2003 Toyota 4Runner Instrument Panel & Glove Compartment