... no grommet around the antenna... how hard could it be for me to fix this myself. Turns out it's more difficult than you might imagine. Does anyone here have any experience swapping out antenna base units? I snapped off the plastic threaded nipple at the top of the unit....

It's actually very quick and simple. You have to remove or at least loosen the base unit anyway to replace the grommet. Just order a new base unit and grommet, and read the DIYs.
The parts:
http://www.ecstuning.com/BMW-Z3-1.9-M44_1.9L/ES182326/
http://www.ecstuning.com/Search/65218411562/ES2608925/
Some DIYs:
http://www.zroadster.net/forum/viewtopic.php?t=8613
http://www.bimmerforums.com/forum/showthread.php?1414102-antenna-grommet
http://blog.bavauto.com/11619/bmw-antenna-grommet-seal-how-to-replace-diy-z3-318ti-convertible-e36/

The visible grommet is an outer grommet, in the fender. There is a larger inner grommet just under the fender in the body, and plastic tip of the base goes through both. The inner grommet does not deteriorate, and will not be disturbed by pushing the lubed tip of the base up through it.

 

Thanks for the links. After snapping off the threaded antenna nipple on the original base unit I retreated and regrouped and thought my next moves through before taking any further steps. I am happy to report the new base unit is installed, the nipple is through the grommet and the antenna is mounted correctly. Everything is solid and looks clean and finished. In my haste to get to the antenna base unit and swap it out I neglected to remember where the two wires on the top motor were attached when I unbolted the unit and put it aside. Can anyone post a link to the top motor schematic that shows the wiring? Thanks in advance for any and all assistance.

 

Thanks, I had the same problem and found this information very useful.

 

Snapped my antenna's neck too...

I did the same thing. Broke off the part into which the antenna screws. So effectively screwed myself and not the antenna.

Bookmarking this post. Thanks!