I'm far from being an authority on this but, in general, you are correct that police reports are public information. However, as seamusTX says, finding any easily-sourced information is going to be a steep mountain to climb.
The primary reason is that police/arrest records are specific to the jurisdiction of the incident. For example, you would need to go through the Open Records Unit of the Public Affairs Division of the Houston Police Department to locate records dealing with incidents/arrests made by the HPD. It will be the same for every municipal police and county sheriff’s department.
And keep in mind that while you can ask for access under the Open Records Act, no agency is required to massage the data for you: in other words, you can ask for access to 911 tapes, dispatch transcripts, jail bookings, incident reports, compiled reports that are routinely maintained, etc., but no agency will have the resources to do the research for you that would be necessary to review past incidents to determine if a CHL was involved, then further to understand the outcome of those incidents.
Records maintained by the District Attorney offices are separate, and may or may not be publicly available depending upon prosecutorial (or civil suit) status. Records that are interagency (e.g., joint county/municipal involvement, incidents that may involve other extradition to/from other states, or involve federal enforcement agencies like ICE or the FBI), are another animal, and things can get complicated very quickly.
The Uniform Crime Report compiled and published by the FBI is completely dependent on thorough and accurate reporting from local agencies. The statistics that DPS maintains about CHL criminal activity are summary only. In neither case do the compilations provide any statistical information about CHL use of deadly force that is no-billed, acquitted or, of course, never reported (i.e., gun drawn and perp runs away without a shot being fired).
Kinda like you, I know there are meaningful data in there somewhere, data that are bound to shed a highly favorable light on CHL holders. But I don’t know of any reasonably efficient way to go about getting at the info, or of any way to show statistical validity if you do.
For anecdotal information, one place to look might be the archives of the NRA’s Armed Citizen reports:
http://www.nraila.org/armedcitizen/. Entries date back to 1958, and are searchable by key word and/or state.