Query performance and join hints, plan cost, and duration
Another option to optimizer hints if you cannot even touch the query is to use Plan Guides.  However, since your query statement is dynamic with many unparameterized tokens, I doubt it's possible.

Since you know your data, I think you're better off just staying the path of query hints.  Statistics have been known to be lies, lies and damn lies.  It can only provide an overall shape of the data, but for specific conditions (e.g. fund_src_name_id values, state_id values, combination of the two etc) it can just produce the wrong plan.