It’s not an uncommon issue in many councils, while some councils seem to process the paperwork almost by magic. Unfortunately, the work-arounds almost all have a high likelihood of creating duplicate accounts for either the scouts, the parents, or both.
What we have done for scouts brand new to scouting is create the scout account with the name, birth date, address, etc exactly as it appears on the application before we submit the application. Similarly, we create a parent account with their name and email address exactly as it appears on the application. Then, we wait for the Registrar to “create” the BSA ID for each person, and hope that member sync catches the existing account. It only works some of the time.
For existing scouts transferring in, we use the “Transfer in Scout” tool to transfer the scout’s Scoutbook record. That only gives 90 days for the unit and registrar to get the paperwork submitted and processed, but we can “work around” the 90 days by setting a new start date on the 89th day so it keeps stretching the time. Once the official roster in my.scouting is updated, we return the membership start date to the actual start date. This has a low likelihood of creating a duplicate account assuming the scout is from the same council, their BSA ID is included on their transfer paperwork, and the “transfer application” box is ticked on the paperwork.