I'd second what odyssey says. Really glad that you're giving it another go (and that they are letting you) - it sounded from what you wrote, that those intros/bridging, was really badly handled.
Incidentally, it could be said that this demonstrates quite some resilience on your part ;)
But yeah, in my limited experience too, the child's SW and the adopters' SW don't necessarily talk much. The adopters' SW won't 'know' the child personally; at most, if they have a well functioning team, the child will have been briefly discussed in team meetings. But quite possibly, the adopters' SW knows exactly what's written in the CPR and medical report (or less, depending on how well they read these docs). As soon as you as adopter have in addition to reading the documents, perhaps chatted to the child's current carers, YOU will know more about the child than your SW - no matter if the child is from your same LA or not.
The person who is really supposed to know more about the child, is the child's SW (in reality though, it is often the FC who knows the child best). So it all depends on the child's SW and FCs. On how well they communicate, and how much they have actually got to know the child. Some SWs have such heavy caseloads that they never really get a chance to properly understand each child's particular needs and issues. Again, the child being in 'your' LA care, doesn't necessarily change any of this!
That said, you and your SW both, now know better what to expect and what kind of things you need to insist on, and I'd expect that any child's SW before agreeing to a match with you, will look at why the last one went wrong, and learn from that too.
I hope you're holding up ok. Pulling out of a placement at the end of bridging must have been incredibly hard, with huge emotional turmoil. It's hard enough saying 'no' to a child who you know only on paper, through a CPR - even though it may be the right thing to do - I can't imagine how hard it must be to make the decisions you have had to.