It must feel really difficult with all these different opinions. Once again I would say, go with your gut. Meet the teachers at the current school and see what they say. Does your instinct say that they may be able to help this time, now that it appears to be your very last stab at it? Could you give it a few months and see if it works?
Three of my friends have experienced this type of clinginess with their children - one in reception, and with two others it developed in later years. In all cases, the schools offered a TA who came and greeted the child and took them in so that the Mother could disappear quickly and it didn't prolong the goodbyes. In one case, the school told my friend that her daughter was absolutely fine once she got in school and there was nothing to worry about. They really didn't see a problem, but when they could see how upset my friend was, and how at the end of her tether she was, they did really step in and help. In all cases it eventually worked, although it did take time.
Perhaps be really honest with the school and say how upset you are about it and that you are thinking about moving her. If they are a good school they will really listen and step up to the plate and try and help. I'm sure you won't, but my advice would be to really try and not be accusatory with the school. Just explain that what they're doing at the moment isn't really working and can they come up with anything to help you give it one last go as it is causing you a lot of stress. I am a teacher and parent and they will respond much better if you try not to criticize them (difficult, I know.)
At the new school, again, I 'm sure your instinct will tell you if it's going to be a place that will really nurture and support your child. I looked around 2 alternative schools for my daughter. Both headteachers showed me around, and after half an hour I could tell which one seemed really interested in my child and which one didn't. I explained the dilemma I was in and the headteacher I liked said I would be really welcome to send my daughter in for a trial day so she could experience the school, meet the girls in her class and make the decision for herself (she is Year 5, so a bit different in that respect I suppose.)
Currently I haven't moved my daughter as it would mean moving house too. I wanted to move her due to some very unpleasant friends who had caused a lot of trouble for her and could be classed as bullying. I was really upset and not sleeping and was thinking about just pulling her out of the school immediately. However, after taking a step back, I realised that I was actually more upset about it than my daughter. When I thought long and hard about it, I realised that pulling her out immediately was more about my anger and was not necessarily in her best interests (she was actually getting on well with some new friends.) I could very easily have got into a big argument with the school and created a very negative exit for her. That's not to say I won't move her in future but I did just have to think long and hard about what would cause the least problems for her (I hate being an adult sometimes. i just wanted to be really petty and throw all my toys out of the pram.
Just remember you're not alone. The school will have dealt with this loads of times before (and way way more difficult things than this.) They'd have to be a really hopeless school to not try and help a really stressed out Mum who just wants her child to be happy (I'm sure that is what they want too.) Don't worry about taking their time - that's what they're there for.