This seems borderline impossible? I'd be curious if there were missing indexes or bad index selection or efforts to do things like joins? Normally for very large data sets you can shard by account if needed if that's the common filter if there is some insane table scan. Audit stuff tends to be "sparse" so if you can get an index which just tells you which pages have results, that is usually a 100X speedup with a pretty small index size.
But agreed, a daily dump to something can go a long way to unlocking other tools - in govt this is especially true not because the DBMS is hard to use, but because so many layers of consultants and others in the way it's not usable.
