I would run manifolds before TTI headers. It’s that simple. IMO they are junk and there are better options. If you are smashing your headers flat it’s because you have issues driving the car with headers.
Never owned a set and never plan to. I have a set of Doug's in the box but am probably using the factory manifolds. TTI is too proud of something they blame the assembly of the car on in regards to fit. My advice is keep working your tooling until it not a problem or don't make someone give up their birthrite for a set of headers they may have to work over to make fit. JMHO and it's just a general statement...