When is this trip? Unless your trip is coming up really shortly, you should be able to go for the Gold challenge. I'm not sure if Marriott just grants these but you can tell them that you plan to stay with Marriott more often if you have business trips coming up.

The benefits apply to you even if booked from Expedia. The points and elite stay credit might not be earned though, but all the other benefits should be there according to your status (Silver, Gold, Platinum).