This can be a hassle with any statewide or large regional system.
However, you are a Premium Subscriber. If, instead of appending in Sentinel, you used software such as ProScan or ARC536, you could select and import only the sites & departments you wanted, without ending up with the whole state.
Aware - and I do have Proscan. The advantage, at least for me, is if I add all, then avoid them it will not add them back if I append them at a later date.
For me, the trick to mass avoid is changing the name to the few sites I want by adding a Z to the beginning of their name, then sorting, Drag and mark avoid, then change the name back. This might take me 2-3 minutes (using Sentinel) and is easier than future hassles.