This should not be hard to troubleshoot. To start, temporarily disconnect one port from the NEC and connect the HT port to an analog phone. Call in, answer the analog phone, confirm that you have clean audio in both directions, then press keys on the calling phone and confirm that you hear clean DTMF tones on the analog set. If not, debugging tools include packet capture on the PBX (look at RTP being sent to the HT) and syslog on the HT.
If the DTMF sounds good, reconnect to the NEC and monitor a call with a butt set. If you hear nothing wrong and still have trouble, one possibility is high frequency noise messing with the NEC – try a DSL filter between them (try it both ways). If no luck, perhaps changing the FXS Tx gain will help.