Will the 1 7/8" and 2" TTI headers fit eagle 5.7 heads?

Run them. I have a 6.1 based 426 with heavily ported early heads that have the square ports. It dynoed just fine with the TTI 2 inch long tubes. Think how far down and how much work it would be to shrink that 2 inch tube to match the port.
I think your correct, the more I look at headers the more companys I see using the round port. I've also seen some porters using the round gasket to open up the exhaust and change the design of the port for more flow. I know this little eagle motor won't need a 2" header but when I build a bigger motor it would be nice not to have to buy new headers. I was also surprised on the port work. I'm going to start another thread on that.
Run them. I have a 6.1 based 426 with heavily ported early heads that have the square ports. It dynoed just fine with the TTI 2 inch long tubes. Think how far down and how much work it would be to shrink that 2 inch tube to match the port.