1) There is no special treatment-privilege-advantage in trying to make a MAW dining reservation.
2) You get in the queue just like anyone else.
3) The ONLY way to bust through the haze is to find a Lobby Concierge (usually 1-or-2 per resort) with Dining-Override-Code.
. . . with the code, a concierge can put any group of any size into any restaurant at any time
. . . the only exception are capacity-limited eateries (eg: HDDR, Luau, BBQ, V&A)
3) Unfortunately those with The Code do not advertise it, so it is hit-or-miss in trying to find the right person.
. . . in many cases, other Concierge will know of the person
. . . whether they let it out is a matter of individual initiative (see notes).
NOTE1: The overrides are meant to squeeze people into even sold-out eateries whether in advance or at the last moment. We usually use the code for a) WDW General Managers and above, b) Disney/ABC vice-presidents and above, c) guests of the Disney/ABC Marketing Department, or d)designated celebrities. Of course, these people can request an ADR even if they are not dining with the group requested. I am a Give-Kids-The-World coordinator of volunteers, and I only use the code VERY sparingly, unless directed to do so for the aforementioned VIP's.
NOTE2: As a MAW family/group, you will have a special button and you might also be escorted by a Guest Services CM. In some cases, the podium host/hostess (aka: "SEATER") might do you a favor and squeeze you in. They do not have to, but many CM's will work with the MAW family.