With respect to the litigation concern:
While there are certainly plenty of lawyers who would be willing to pursue such a case, the fact remains that for anyone to get past the initial filing of such a suit there must be actual damages; the act or fault must have caused the plaintiff some actual harm. The woman who succeeded in the famous McDonald's hot coffee incident was harmed by the hot coffee; whether the harm was serious enough to warrant the judgement is another matter, but there was no question that there were actual damages. The first thing any lawyer, plaintiff or defendant, is going to do is ask, "What were the damages?" If the answer is none, then there's no case.
And that's the issue with the chainfire. I know that it's a popular internet pastime to rant about chainfires, but you really have to dig deep and long to find any instance of damage done to the firearm or the shooter. I conclude that fear of possible litigation from a chainfire incident was not a significant factor, if it was even considered, in deciding whether or not to put this gun into mass production.
In any case, the issue here is not a chainfire at all, at least not in the classic sense of sympathetic firing of adjacent revolver chambers. You've correctly identified the issue of setting off the back charge in conjunction with the front charge, but I don't think the term chainfire applies.
My opinion is that the odds of firing both charges are probably quite high. And the results are not good for either the gun or the shooter. There are plenty of anecdotes on the internet about accidentally double charged (meaning two charges and two projectiles, one atop the other, as opposed to double shotted, which means one charge, two projectiles) rifles and the damage done to the barrels (and shooters) in such incidents. Double-shotting was frequently and intentionally done in battle to good effect. Double-charging was not. The bottom line is that the top charge acts as a bore obstruction for the bottom charge, and the pressures become quite high. The saving grace here, if any, is that the chamber is very short and there is a pressure relieving mechanism at the chamber mouth. Still, the physics are not good for continued long life and happiness of either the gun or shooter.