Yes. First, the decision to use --with-curl=/sw is the correct one. Since fink doesn't delete files, the (old) Apple installed curl in /usr/bin still lives on your machine and the PHP configuration program is picking it up instead of the (new) fink version. (The configuration process and $PATH are independent of each other.)
So, you need to manually add the /sw directory to point PHP and cURL 7.10. Once I did that, I got an error that essentially boiled down to "can't locate file for: -ldl" I did some poking around and the short answer is: I didn't have a necessary library installed.
Using fink to install "dlcompat-dev" fixed the problem. (I already had dlcompat and dlcompat-shlibs installed.) Once I did that, PHP compiled with cURL just fine. (Well, it did give a warning about /lib not being found, but that's harmless.)
Let me know if this fixes your problem or if you're still stuck.