You could also get them back on track by having the castle still crash. Either forces on the castle try to take over, or Blagothkus realizes the error of his ways (supporting the dragons) and crashes it intentionally - he is the only one who can control the castle after all.
Boom. You are right back at the beginning of Rise of Tiamat.
It never sat well with me that a giant - sworn enemies of dragons - is helping Tiamat's cause. I changed Blagothkus's character and motivations a lot when I ran it.
Me too - I had it so that his wife's spirit was being held hostage by the cultists so he had to do their bidding under duress. The PCs had to defeat the cultists (and an Ice Devil) to rescue her and win Blagothkus's trust. That was a fun encounter.