Is there a way to get an installed RPM's signature Key ID programatically?

To answer the actual question, no, there is no way to directly query for the keyid. I ran into the same problem you're having and found someone actually created a bug report with redhat for a feature to request that feature be added.

In the bug report, the responder says to use something like below:

rpm -q --qf "%|DSAHEADER?{%{DSAHEADER:pgpsig}}:{%|RSAHEADER?{%{RSAHEADER:pgpsig}}:{(none}|}| %{NVRA}\n" emacs | cut -d' ' -f11