Joshua would do well. His power, size, and consistency would make him a big threat during the 80s. In one-off prime vs prime match-ups, it's more than possible a couple of these guys beat him. A handful of them are more talented and more fluid boxers than Joshua, but the majority of the 80s crowd just couldn't put it all together or lacked the necessary dedication or consistency to really make it at the top level. Joshua clearly beats Berbick, Biggs, and Cooney at the very least though. If Tubbs and Witherspoon show up fat like they did fairly frequently then there's a decent chance Joshua beats them as well. Thomas before all the drugs and injuries is a favourite over AJ imo. Mid-80s Thomas vs AJ is 50-50. Tucker is a live dog. Douglas probably loses unless he can miraculously motivate himself into shape like he did against Tyson. AJ would do well but we won't ever know for sure of course.
Grant is all the worst things you claim Joshua is and then some. A muscle-bound glass-cannon, a front-runner who was stiff and upright with a chin of wet paper. I'm pretty sure you've used all these exact words to describe AJ and all are far more true for Grant than they ever were for Joshua.
I think he's favored against most of them, although, it all comes down to consistency. How many twinkies has Page eaten in camp? How many pipes has Tubbs had? If Pinky shooting junk in camp? And which version of Joshua shows up, for that matter? I favor AJ but not putting any money.