The attorney pled with the company ... saying that instead of fighting the lawsuit, they should embrace it and do the right thing by the ladies he says are affected. Speaking of them, a few stepped up to the podium and delivered incredibly personal remarks.

One woman broke down in tears remembering her grandmother, whom she says died of ovarian cancer she claims was contracted after using J&J products. Another woman said her usage of the talcum-based J&J powder had started from a young age, and was something deeply embedded in her and her family's hygiene routine ... as a direct result of the advertising and literature she says they'd been fed over several years.

Based on how J&J has reacted thus far, though, it seems this case may go to court ... despite Crump's cry for understanding.

9:42 AM PT -- TMZ just obtained the lawsuit Ben Crump and his associates filed against J&J ... and, boy, did they deliver on the goods.

The suit is damning on its face, with claims of a mountain of evidence and studies dating back to the '60s and '70s (which apparently continued on through the '90s) clearly finding that talcum and talcum-like particles appeared to be naturally carcinogenic, easily mobile once in the body and most importantly, cancerous and dangerous to human health.

Crump cites over a dozen case control studies done by several different health orgs and science groups looking into how talcum was affecting women ... and, time and again, Crump says the studies often landed on the same conclusion -- namely, that talcum seemed to be linked to ovarian cancer that had developed in ladies who'd used talcum-based products.

He goes on to say these studies and findings were widely published and easily accessible, going on to further allege J&J were well aware of it ... and yet, continued to push Baby Powder and Shower to Shower powder -- both of which are talcum-rich.

Then comes the true bombshell ... and that would be a detailed accounting of what Crump describes as a calculated effort -- spaninng at least two decades, if not more -- to go after African-American women, who turned out to be one of J&J's largest consumer bases to use their talcum powder products.

Crump claims to have obtained internal marketing presentations, in-house data and even proposals drafted up between J&J and outside firms -- all of which he says conclude the same thing ... that Black and minority women were "highly important to business" and that company "need(ed) to maintain" their cash cow, while also allegedly acknowledging it was becoming “difficult to efficiently retain core AA consumer.” AA, Crump says, was how J&J referred to African-Americans amongst themselves.

He goes on to say that among their strategies for getting Black women to continue buying their talcum powder products was the continued tactic of stopping in at churches and salons in predominantly Black communities ... and handing out free Baby Powder samples. But it was more than just on the ground, person-to-person interactions, Crump claims. He also alleges J&J considered recruiting Aretha Franklin and/or Patti LaBelle to be a spokesperson for them in the mid-2000s, for the sole purpose of catering to Black women, and to have them continue being loyal customers.

Unclear if the Franklin/LaBelle idea ever materialized, but it's just one example of what Crump claims J&J were kicking around to keep their grasp strong. On top of that, he says they put out Baby Powder/Shower to Shower ads on radio stations with predominantly Black audiences. In short, Crump says J&J were well aware of who their main clientele was for their talcum goods, and they went to incredible lengths to push it on Black women by several different means.

Because of that, Crump says a countless number of African-American women, including women from the National Council of Negro Women, contracted ovarian cancer ... and endured pain and suffering, loss of enjoyment of life, and in many instances, their actual lives.

He's asking for a court to sanction J&J over the alleged targeted campaigns, by forcing them to design a system to monitor who's been adversely affected by their talcum sales, track their medical needs and to reimburse them -- not to mention new ads to address what Crump says J&J did to the Black community. Of course, he's seeking damages as well.

In response, J&J says they empathize with anyone suffering from cancer -- but deny their products are the cause of it, explaining ... "our products are safe, do not contain asbestos, and do not cause cancer." They say the accusations against them in this suit are false -- adding that the idea they'd purposefully and systematically target a community with bad intentions is absurd.