You also played 3-4-3 in April 21, how did that work out? It was at your backyard, too, although you could argue you didn't have your full squad available.
IMO, the 3-4-3 worked while it was a surprise or other teams weren't accustomed to it. Very prone to counterattacks, and without the proper defenders becomes a major weakpoint. The 3-4-3 in part did have an effect on your problems, especially early on in the season. The Sociedad game comes to mind, both of their goals were counter attacks, especially the second goal (Okay, it was a major Villa screw up). Once teams realize the 3-4-3 is defensively weak, they could just sit back and kill you on the counter.
Villa Falcao Pedro
Messi
Iniesta Xavi
Busquets
Abidal Mascherano Puyol
You removed one of your best players, Dani Alves, from that formation you just posted. IMO, he's one of the most important pieces, in that with him you can easily revert between 3-4-3 and 4-3-3.
Like so:
Villa Falcao Pedro
Messi
Xavi Busquets Alves
Abidal Mascherano Puyol
Of course, this also removes Iniesta, but that's the only way I see that Alves, Xavi, Messi & Falcao could play together in a 3-4-3, with Busquets (who you're so fond of) keeping his DM spot. Still a 4-3-3 wouldn't work, only a 4-2-1-3 variation with Messi in regular #10 role. Unless you sacrifice one of Pedro, Villa or Messi for Iniesta.