Lesley,
I've changed the subject line to reflect the name, place and dates; this will help other Meyer researchers find you.
Please pardon if the following info is already familiar to you.
You probably already have been to vifamilies.org, no? If not, there is info on the Brucker family here that mentions your ancestor. (This was Maria Elisabeth's second marriage.)
http://www.vifamilies.org/blistings.html.
There is considerable info on the West Indian troops, so I would pursue that lead. Check the PRO in London too.
From the listing of the marriage, I would guess that "v. Meyer" might be "von Meyer." You could add that to your search names.
You probably know by now that birth certificates are largely a 20th century idea, though Napoleon did have civil registrations in, for example, Alsace Lorraine. Maybe others familiar with St. Thomas will pitch in here and let us know whether there was some sort of Danish registration beyond the census that was peculiar to St. Thomas.
Otherwise, the best place to dig is into church records on microfilm.
Are you familiar with the Mormons' Family History Libraries? If not, go to
www.familysearch.org. You can also use their new search engine at
http://pilot.familysearch.org/recordsearch/start.html#p.
On the familysearch site, select Library catalog and then put in the place, St. Thomas, Danish West Indies (or you may have to use US Virgin Islands). You will find the films you need to order for the churches in St. Thomas at the time.
Hope this is helpful.
Laura