"have long established" is correct and usable in written English, especially when referring to something that has been established for a good length of time.
For example, you could say, "The traditions of this village have long established roots."
Neuroscientists have long established that writing and reading are handled separately by the brain.
Astronomers have long established a correlation between the pulsations of these stars and their absolute brightness.
The question is legitimate, not only because historians have long established how, in his rise to power, Hitler took Mussolini as a model.
Traditional film studios have long established a system of showcasing a movie in theaters followed months later by the release of a DVD.
Cornell University, the SC Johnson College of Business and the Accounting program have long established relationships with many major employers, including professional service firms, consulting firms, banks and fortune 500 companies.
"We've always know that xenophobic attitudes prevail among up to 20% of the population in our country – just like in other EU countries, where far-right parties have long established themselves.
As brain science has long established, the child and early adolescent brain has unique plasticity and dynamism.
Cornell University, the SC Johnson College of Business has long established relationships with many major employers, including professional service firms, consulting firms, banks and fortune 500 companies across a broad range of industries.
Meyers has long established a reputation for lineny upmarket wish fulfilment; it's yielded its cushiony comforts in the past, but has never seemed quite this blinkered.
International law has long established that denying reproductive health services to women in life-threatening situations is a violation of human rights.
