this is a cheap fix really, its clear its the diff thats the problem and you need a longer ratio diff. I had the same problem when I changed my gearbox to an M3 gearbox, I had to find an M3 diff and fit it to an e30 casing (fitted the M3 box to an e30).
Ignore the comments about the wisdom of converting to manual, it was a good decision as once an automatic gearbox gives you problems it never stops giving you problems, check the e30 forum for many examples of people converting their boxes to manual.
There is a place in Paarden Island that does good work on gearboxes, I don't know the name of the place but I can find out for you today. Alternatively take the car to Autowizards in Maitland (reopen 6th January) and they can source and fix all problems related to this issue on your behalf, they also have access to BMW parts at good prices as they are close friends with a guy two roads away that just sells BMW parts.