Should I settle or consolidate my $35k in credit card debt?

It's really hard to say if you should settle or do a debt management program. You say you have 35K in debts, but it really depends on what you both are making. If you are totally overextended even with a better loan on your cards, I would say debt settlement is best for you. If you can make it with a better loan and lower payments, then do debt management.

Please provide more details as there are some very smart people reading these forums.

If you can afford you minimums payments and just need one payment with lower aprs than go with a debt management Plan. If you dealing with a hardship and thus overextended than you may want to consider debt settlement because your bills are either about to be late or they already are. It will get you one low monthly payment about half of what you were paying.