Unfortunately, the database isn't showing if the two nearby sites have multiple transmitters with the same frequencies. There is something broken.
For the OP, both of the sites in his parish, Avoyelles, as well as the majority of the sites in the adjacent parishes, use licenses issued to the state, and as such are not tied to a specific site license. This makes it almost impossible, if only using what little specific information that can be obtained from the state license, to determine which sites, if any, are simulcast.
As you've already suggested, perhaps a move to the state forum might find someone more local to the OPs location, who may be able to clarify whether of not simulcast is a possible issue. If a needed site is simulcast, then the best options are one of the SDS series scanners, the P25RX Blue Tail receiver, or a Unication pager.