Hi Mike,
Network does not always work on such complete structures, but may work with portions.
(Having a lot more U and V curves may prevent Network from working.)

After creating the UV curves,
1. Place a point at the origin. This is not essential, but helps locating the origin.
2. Select only the curves passing through the origin.
These are the U curves, and could have been identified by previously running a separate U mode. (It is not essential to run a separate U mode.)
3. Run Trim command
4. Press "add trim points"
5. Select origin point as place to put the added trim point.
6. Press Done. (Do not press "remove curves" button.)
7. Press Done again. The two "lobes" are now separate.
8. Select both U and V curves for one entire lobe.
9. Press Network, which creates one lobe surface in half a second or so.
(Network does not work if both lobes UV lines are selected at the same time.)
10. The second lobe can also be Networked separately.

- Brian