Paraboloid complications

I tried printing a paraboloid, but the lines were too thin, as thin as the supports, and thus the shape came apart on trying to remove supports.

Which made me wonder: How long is it possible to make unsupported bridges ie. hanging sections without any support. The following link indicates that at least for the replicator 2, 10 mm is reasonable, and here they were able to do up to 40 mm. I do not know if this is different for the 5th generation. I will find out: I am currently reprinting a fattened up version of the paraboloid without support. The bridges are more like an inch. I am printing it large side down so things will only get closer as time passes.

Here is the fattened version, printed without support:

Improvements: Perhaps too reminiscent of a famous 3D clothing item from Shapeways. In addition, more attention needs to be paid to the join points. There may be a possible fix in Mathematica. Alternatively, it might be necessary to have an intermediate step between Mathematica and printing. In case that doesn't work, here is a possible solution using Tinkercad. Here is a close up: