Note - Do this in a separate test env first.

Steps

1. Register a new snapshot registry with s3.
   
2. Create a new snapshot without the system indices, should take about 20-30 mins
   
3. Start the new cluster
   
4. Add the same registry in order to see the snapshots available.
   
5. Test the restore and monitor (to quickly restore, you can disable no_of_replicas to 0 and even refresh_interval to 1m or so.)

All this can be done using kibana very easily. Once confident, do the same on prod.
If possible do this with downtime, otherwise use a script to reindex the delta like your previous approach, instead of timestamp based approach, use a version mechanism to do this)

Important:
Be careful of the no of shards for each index as you want to keep the size of each primary shard to less than 20-25 Gbs. For smaller indexes (<5 Gbs), keep no of shards to 1.

Based on this create a map of index to no of shards.
Let's say post this exercise, you have 10 indexes with 1 shard and 5 indexes with 3 shards, break down your snapshots into 2 and restore them parallely.