The inter-MSC handover can be divided into 3 cases:
1) Basic inter-MSC handover, where MS is handed over from MSC-A to MSC-B.
2) Subsequent inter-MSC handover, where MS is handed over from MSC-B to MSC-B’.
3) Subsequent inter-MSC handback, where MS is handed back from MSC-B to MSC-A.
In the case 1 and 2, the MSC-A controls the call and maintains the connection from MSC-A to MSC-B or MSC-B’ during all time of the call. Only in the case 3, the MSC-A will release the connection between MSC-A and MSC-B after handover procedure.
I could confirm that the LU can only be executed after the call is finished. In the scenario you have mentioned, the busy announcement is not the problem as the MS may have the Call Waiting subscription. However, plz be noted that the LU procedure is performed via SDCCH, not by SACCH nor FACCH. Hence the LU can be performed only after the end of the call. Updating the SIM of the MS with new TMSI and LAI will be processed simultaneously with the LU procedure.
About inter-PLMN handover, I have no new idea yet.