As you suggested, the problem is probably focused on LU only. During Location Updates, the SDCCH is dropped.
Please please please, investigate this issue with traces and
1/ confirm the drops occur only during LU or IMSI ATTACH
2/ isolate the IMEI / IMSI of those mobiles
3/ see if there is a correlation (always same brands / models of phones, for example)
The E2E CSSR is great for this alternative use, as you did : you can isolate sd drops during call setup and sd drops during other procedures.
(note: i think these sd drops during LU are a worldwide issue, there are some threads about this in this forum… some ZTE phones seem to have some issues (based on older threads), but perhaps others too)
Have a good day,