marriage isn't binding until its consummated (part of why the wedding ceremony included the "bedding" so that people got to see for themselves that marriage was consummated), which is a big reason why Tywin has put so much pressure on Tyrion to knock up Sansa and secure the north, as Tyrion refused the bedding.
So yeah, Cersei would have the highest official legal title right now (although whether she has the power is a different argument)
the Lannisters don't have the debt, the Throne does (King Joffrey Baratheon, not Lannister). If the Tyrells took control, Tywin could easily side with the Iron Bank by saying that he would have been able manage the kingdom to a point where the Iron Bank could be repaid, but that the Tyrells messed that all up...
I don't think the Tyrells are dumb enough to take that on, not with Lady Olenna still alive (and Margaery also appears to be rather cunning)
sounds like you just made a solid case for it being a fitting death