How is it possible to parallelize a hashing function to crack an iteratively hashed password?
The bit about parallelization is not for hashing one password. But the attacker, by definition, has a lot of passwords to try, and these can be computed in parallel, provided that the function maps well to whatever parallel architecture the attacker would like to use. In the case of the multi-SHA-1 method you describe, it maps very well on GPU. Note that the same can be said about PBKDF2, which is why I tend to recommend bcrypt, which is more resilient to GPU.

Although I do not immediately see any obvious problem with your SHA-1* function, it has the generic issue of being homemade and of not having been investigated thoroughly by dozens of cryptographers during several years. Therefore I would not trust it.