In case anyone else is interested in researching rabbinical genealogy
in Galicia or wants to know the rabbis of various towns, these are the
suggestions I received in response to my question about sources.
Unfortunately for me, there is very little available in English.

Meorei Galicia (Encyclopedia of Galician Sages), 5 volumes, compiled
by Rabbi Meir Wunder contains genealogies of Galician rabbinical
families, listed alphabetically by surname. For prominent rabbis of
each family there is additional biographical material, including
rabbinical compositions, responsa correspondence and photographs.
There is also a town index. It is on-line at
http://jgaliciabukovina.net/limited/digital_books but you have to pay
a small fee to join to get access. It is in Hebrew, but there is a
name index available in English on Gesher Galicia.

Another truly comprehensive book is Otzar Harabanim, compiled by Rabbi
Nathan Zvi FRIEDMAN, which contains 20,000 entries covering the period
930 - 1970. Entries are arranged by first name and then by surname,
with surname and community name as "book name keys". It too is in
Hebrew. I don't know its availablity.

Letoldos Hakehillos Be'Polin lists rabbis in Poland by town.

The Biographical Handbook of Rabbis is a bibliographic directory of
all the rabbis since the Enlightenment who worked in or came from
German-speaking countries. It is online at
http://www.steinheim-institut.de/wiki/index.php/Biographisches_Handbuch_der_Rabbiner_%28BHR%29
[or http://tinyurl.com/gwwcdbn --Mod.]
It is in two parts:
Part 1: The rabbis of the emancipation period in the German, Czech and
Polish large countries, 1781-1871 contains entries for 1,952 rabbis
who were employed in or came >from the German Bundestag and the East
Prussian provinces and Part II: "The rabbis in the German Reich,
1871-1945". Each part can be downloaded for free, but it is huge and
the download would take quite a while (my computer was estimating 4
hours and I have high-speed internet). It is in German.

Gesher Galicia's All Galicia Database includes a few different List of
rabbis >from the 1860s

Another source that has been suggested is the B/M/D registers for each
town. These were submitted to the state annually, and were signed and
sealed by the official "chief rabbi". The officiant at the bris or
wedding should be noted on the record. The Mormons have microfilmed
many of these registers, so they could perhaps be found in the
FamilySearch catalog.

Judith Singer