I can't invest the time to read all the responses, but I think this is a very interesting dilemma/discussion that I wish I'd read sooner.
OP, from what little I've seen, you've gotten a lot of flack from people who feel defensive of the mother/child and who seem to think your fiance is a monster, for wanting to terminate his parental rights. But this is what I hear in your posts (the ones I've read), and it doesn't sound so monstrous, to me:
>> He feels tricked and trapped, because he intentionally and responsibly chose not to have a baby with her, since neither of them were financially capable of providing for one; he believed they had taken precautions to ensure there was no pregnancy; and, given her trash-talk, he suspects she lied to him and intentionally sabotaged contraception - even before they broke up, when he still trusted her and felt/was intimate with her - all as part of her stated plan to "ruin his life".
And YOU feel cheated because none of this was part of the picture when you fell for him; and rather than the child being a secret he kept from you (in which case, you might say, "I guess I didn't know him as well as I thought I did!" and break up), the child seems like part of an outsider's plot to hurt your fiance (in fact, the mother has said as much). You and he have a plan to become more financially stable, together (perhaps be able to start your own family) and this definitely threatens that plan. It's not that you resent the child herself, but all the adult circumstances surrounding the child seem very unfair and you feel scared about what your/finace's life will be like if he starts paying support, when it already seems pretty hand-to-mouth, as it is.
Well, as you've presented them, these circumstances ARE unfair and your/your fiance's feelings are understandable. Even members who feel duty-bound to defend all other moms should be able to take a minute to acknowledge the frustration of the situation you - also a fellow woman - and the man you love find yourselves in!
That said, of course, as adults, you guys are saddled with the obligation to rise above your feelings and try to do what's right in the situation you have, even when it's not what you feel you deserve.
>> But, in thinking of terminating his parental rights, your fiance is hoping to do right by the child, not just selfishly avoid child support. The mother is devoted to "ruining his life"; has taken the child to live in the furthest point in the country from the father; the father cannot afford to visit there, nor fly the child to FL for visits; and the mother is clearly unmotivated to facilitate contact between father and child, when she's in FL. So, there is no father-child relationship, right now, to be lost/mourned; developing such a relationship would be extremely difficult; and you can reasonably expect the mom to sabotage any efforts he does make. In your fiances's mind, the best answer is for mom's new fiance to adopt the child and become "Daddy" and for the child to live unburdened by the confusion of having a 2nd father-figure, whom she rarely sees, and about whom her mother tells her terrible things. Financially, if your fiance "struggles just to feed himself", then the amount of child support he would be ordered to pay will not substantially change the child's circumstances, anyway. After all, you can't force blood from a turnip. In these particular, unique circumstances, the peace and consistency of the child having an intact, uncomplicated family (via adoption by the new fiance) might be well worth the loss of the minimal financial contribution by the OP's fiance.
When a mother gives up a baby for adoption, we don't say nasty things about her looking for someone else to shoulder her financial responsibility. We praise the selflessness of her forgoing the personal gratification of a relationship with her child, because she admits that someone else could do a better job of parenting him/her. We acknowledge that she's putting the child first. It sounds to me like this is what the OP and her fiance would like to do.
But your fiance's solution is only best if the mom's fiance actually adopts the child, and if the mom never tells the child, "Your real dad lives in FL, but he doesn't care about you." Even if your fiance could voluntarily sign away his parental rights, it still would not ensure either of these things. In fact, given the mom's hostility, it is almost certain she will tell the child negative things about your fiance. In that case, the best thing for the poor child is to have whatever contact your fiance can get with her, so he has a chance to tell her he loves her; to tell her he's doing everything he can to get access to her - both in person and over the phone - and that he does send her mom money to help take care of her. Hearing these things from him will help combat the opposite information she will hear from her mom. Since the child will spend more time with her mom - and since her mom sounds unstable - she may be inclined to side with her mom. But at least there will be a question in her mind, when she hears, "Your dad doesn't love you. He doesn't want to see you. He's a deadbeat."
Surely you understand: Now that the child exists, despite understandable resentment your fiance has about the circumstances - and despite his reasonable ideas about keeping himself (and the conflict btwn. him and the mom) out of the picture...the FIRST priority must be what's best for the child. That is why the court won't let him walk away. All the deception and selfishness in the world, on the mom's part, don't change the fact that a child exists and needs support, so legally mom's jerkiness and the unfairness to dad are rendered irrelevant. If the child isn't adopted by another man, it's in her best interest to have whatever support both parents can provide, not just one.
Fair or unfair, as adults, this is what you and your fiance must accept and plan for.