It also states that the customer will not own the code, and that it will be contributed to the project under the same license as the project.

I've sometimes had, for odd reasons, customers who prefer to own the copyright of the code I write but are willing to licence it back to me under the GPL. So that's another option.

Oftentimes we charge a lower rate for this sort of thing, since they won't get any IP out of it.

Ditto. I've found this works best if you express it as a "discount" for the GPL code, rather than a premium for getting IP. YMMV.