That's valuable, but cranking statistics up to 10000 and/or creating custom statistics can go a very long way to helping the planner understand the dataset more fully.
The "make it work work perfectly from just statistics" can come later, when time is more flexible. Probably on an identical non-production copy of the environment, if that shows the same performance characteristics. ;)
The planner/optimizer is good at its job. In general, better than I am. If I can inform it about a particular shape of data, all queries around that data will improve. If I tell it exactly how to execute one query, only that query improves.
Additionally, setting statistics to 10000 is really easy. Easier than tweaking a query. Creating custom statistics is more work and may or may not be worth exploring as a quick fix. But if you know the data is shaped irregularly, why wouldn't you make sure the planner knows about it?