You can certainly pick up your own luggage (I'll let other advocates talk about the 'missing out on the best part...' issue

)
Don't attach the yellow DME tags - throw them away.
Go to baggage claim, wait for and pull your bags
Proceed to the DME counter, check in, bring bags to bus, don't forget to tip driver when you get to your resort because he/she handled your luggage.
Check in, go to room, unpack.
I will point out two things, though. First, in 2005 alone the airlines misdirected over three million pieces of luggage and permanently lost over 250,000 of those - so it's interesting that your DF trusts the airline to successfully transport your luggage several hundred or several thousand miles, but not DME to get it the last twenty or so; which brings me to thing two - between when your luggage is removed from the plane and when it arrives in your room, the tags are scanned (and the scans recorded for tracking purposes) five times AND the trucks on which they're transported are equipped with GPS. This information, combined with properly-tagged luggage being pulled between the plane and the terminal before ANY luggage shows up on the carousel pretty much eliminates any bags being stolen. That's actually a more likely scenario, even accidentally, with luggage that does go on the carousel - since many bags look alike and it's possible for someone to walk off with the wrong bag, thinking it's theirs.
eta: I
started typing before CleveRocks posted, but I had more to say so his response appeared first.