I will tell you that since you are using the "free" version of DSDPlus, it is very likely that this ancient piece of software does not decode everything about a TIII system that DSDPlus Fastlane would. It may not be able to properly/fully identify all TIII-related stuff in the datastream. The Free version is probably 8 years old by now, long before TIII systems were popular.
I know that ultimately it sounds like you want to get SDRTrunk working. So maybe you don't want to spring for (pay for) the DSDPlus Fast Lane version of DSDPLus. But if you enjoy / planning on using DSDPlus to sleuth out modern trunked systems, I'd highly recommend you get the paid version. The version you are using just isn't going to accurately depict everyything about a TIII system.
I know that ultimately it sounds like you want to get SDRTrunk working. So maybe you don't want to spring for (pay for) the DSDPlus Fast Lane version of DSDPLus. But if you enjoy / planning on using DSDPlus to sleuth out modern trunked systems, I'd highly recommend you get the paid version. The version you are using just isn't going to accurately depict everyything about a TIII system.