Depending on where you live (I can't tell if you live in NJ or were just citing the NJ case), adoption costs vary WIDELY. If you happen to live in NJ, they may be on the cheaper end because there are pretty substantial legal protections there (and this may be why such a suit went through, but I'm not an expert on NJ law by any stretch). In some states, second parent adoptions are "easy" enough that you can even do them yourself with some know how and an example from a friend. So do check around locally before you assume a second parent adoption is out of the question, and certainly don't do anything that will jeopardize an adoption down the line, should finances improve. Really. I can't overestimate how much it means to me as a non-bio-mom to have that protection. In MA, where they are fairly easy, and yes, you do need one in addition to marriage to be protected during travel or a move, costs range from $500-$2000 (I've only hear the $500 number from one person though, they got a deal).
From another thread though, your partner is Trans right? All of my answers assume a same-sex couple (as viewed by the legal system), so depending on your partner's status with regard to legally recognized gender, this all could be different.