Hiya James,
I can't help you much with details of access to Romanian caves, but I did go caving in Romania many years ago and did some exploration in Pestera Sura Mare.
Two or three years ago I met a Romanian caver at Hidden Earth, and she gave me a little book about the cave, which gives some information about access. According to the book "access to the cave is permitted only with written approval issued by the Commission of Speleological Patrimony and the Administration of Gradistea Muncelului-Cioclovina Natural Park" (for what that's worth).
Anyway, it's a spectacular resurgence cave with a fair-sized stream emerging from its very impressive entrance, which is about 42 m high a 8–12 m wide. The first section of the cave involves walking up the stream. I do recall a section with deep-ish water, but after so many years my memory's a bit hazy! We had problems with flooding after a humdinger of a thunderstorm, but if you can organize access it's well worth a visit.
I'd be happy to lend you the book, which gives a brief history of the cave's exploration and contains a selection of nice pictures, if we can arrange some method of doing so.