I'm gonna have to steal my idea from an independent wrestler named Zac James who wrestles for PWP in Iowa. He once had a contract similar to MITB, where you could challenge for any title at any time. He started off the show by interrupting the Heavyweight Champion, flaunting his contract and option of having a title match whenever he wanted, then cleverly challenged for the title right there by saying "So how bout you give me a title match?". He lost, then later that night cashed in the contract to win the Tag Team Titles with his partner. He technically asked for a title match, and the champ agreed under the assumption he was cashing in the contract and had no choice.
I could see something like this just being shocking at Wrestlemania. As much as WWE would like to make someone the likes of Undertaker or Cena the first (new) Undisputed Champion.. I say just look at what it did for Jericho. It gave him something to brag about, and he's done it for the last decade. Speaking the words, "I beat The Rock and Stone Cold in one night to become the first Undisputed World Champion" was all he had to say to legitimize himself in any situation. And I think it should be just the same in this situation, someone young or at least someone who had never been champion. Either a heel, or a face they wanna turn heel. It could all literally happen in one night.
As much as I don't care for him, I could really see Wade Barrett being the perfect guy to pull that off. Maybe even Cody Rhodes if he was built up as a potential title contender before hand. And thinking about it, even though I said it had to be someone who had never been Champ, even someone like Swagger who isn't even in the main event anymore could be a good candidate. Or a person like Punk who, yeah, is an established main eventer.. but it still always feel like he has to prove himself, kind of like Jericho had to. But for arguments sake we'll use Barrett.
Say the first match of the night, Barrett wins the MITB briefcase. Then as we get to the final matches of the night, you got the World Title Match, a head lining match, then the WWE Title Match. Wade first strikes after the face World Champion just went through a grueling match where he successfully defended his title and vanquished a long time rival. Barrett comes strolling down boasting with his briefcase, saying he can have a title match whenever he wants. He then asks the champ, "So how about you give me a title match right.. now." In the champs head, this guy is cashing in, so he doesn't decline or try to leave, he just tries to fight him off, eventually failing and losing the title. Barrett celebrates with the World Title, picks up the briefcase, and leaves. Well now the fans have already had a shock for the night, and WM isn't even over yet!? Now on to the WWE title. Face Royal Rumble winner just beat the champ and now celebrates with his new title when Barrett comes bolting down the aisle with the World Title around his waist and the briefcase in his hand. He smacks the case into the back of the WWE Champions head, and announces he's cashing in his contract. The ref would decline, Wade would quickly explain himself, to which the ref would realize he was right, then start the match. One finishing move later, and Barrett is standing tall at the end of Wrestlemania with the World Title in one hand, and the WWE Title in the other.
Though Barrett would only be Champion and MITB holder simultaneously for one night, I think that'd be better then have him carry them both around for a while, because I think everyone would eventually figure out what would happen. So not only could he brag about being Undisputed Champion, if he wanted to get detailed with his list of accomplishments, he could point out being the only man to hold the MITB and World Title at the same time, or the only man to win the MITB, World Title, and WWE Title all in one night. It all works, and is an ideal way to unify the titles.