Why isn't work being done toward increasing our own production of it? I'm sure it has nothing to do with patents and money and such.

There are some very good candidates. Looking in my "further research" file pile, I came up with melatonin, deprenyl (selegeline), and Vitamin D3 for starters.

Keeping in mind that each of these is jst one piece of the puzzle since they aren't full fledged human trials:

In a test tube, Vitamin D3 increased cell output of GDNF by a factor of over 18-fold!!! or "significantly" as they say. PMID: 8930983

Again in the lab, deprenyl had a more modest effect but did show an increase. That may be one reason it helps us in addition to MAO inhibition. PMID: 9726430

Melatonin also showed an increase. There has been a lot of work with it for sleep problems and even the NIH says it seems OK, plus it seems to get past the BBB. PMID: 11930164

Also, 5-HT, the serotonin precursor, showed positive effects but my own experimentation with it was unpleasant. But that would explain the reports of anti-depressants triggering neural growth.

Maybe someone with a lab might be persuaded to follow up on this approach?