The concerns about PED's are typically about everyone using PED's during that era, not Biggio specifically. Tainted the era, thus, everyone from the era gets blamed.
He'll get in, probably on the next ballot. Biggio wasn't a good postseason player, probably because he was past his prime by the time the Astros got to the postseason. But he's statistically right in the middle of other second basemen who've made the hall, with guys like Alomar and Sandberg very close to Biggio's production. The fact that he also played catcher helps his cause. And that he is a decent human being, unlike a lot of the other 1990s candidates.
As for Morris, I'm not sold on him deserving the HOF. The fact that his HOF voting numbers drove up from his first year of eligibility until now shows lip service to why guys like him should be preferred over the steroid guys, but that's more as a punishment to the steroid guys than actual accolades for Morris. He had a great World Series game that everyone remembers him for. And that's about it. He was good at chugging up innings. His career WHIP is about the same as a #3 or #4 starter. If longevity and innings is what it takes to get into the HOF, then guys like Mussina, Tiant, and Hershiser would be in there too. I honestly don't think the veterans' committee will get him in later, either. Rubbed too many people the wrong way.