When you say the symbiote is only a psychological villain I think you're selling it a bit short. Think of all the great movies villains. Hannibal Lecter, or the Joker for example. They're both extremely psychological. You could expand into a wide variety of ways to show how the symbiote influences Peter. Have it begin to give him nightmares, and you could really play around with what kind of nightmares would most effect him psychologically.
And the Harry/Goblin conflict is much different than the Norman/Goblin conflict. Norman was out for power, while Harry is out for revenge. A completely different story there. You could expand the things Harry does to get back at Peter. Basically, I would have Harry do what Venom did in his first appearance in the comics, begin to stalk Peter, and randomly show up at places to throw him off. Pete comes home to visit Aunt May, and Harry is there helping her with the laundry, ect. ect. Build the tension with that more.
And throughout this we would be making Brock a much more interesting character. I would actually give him Sandman's backstory, with minor changes. Brock is not a struggling single father, who's wife left him because he couldn't stop the gambling and drinking. His daughter is sick, but he can't pay her med bills because he's squandered all his money with the gambling. He also owes some big deubts to some very bad people.
However, he's not exactly the nicest guy. Eddie's kind of a prick to everyone, except his daughter. She's his world. He gets desperate, and decides to steal some of Pete's photos. Pete (under the influence of the black suit) goes nuts on Eddie and gets him fired. With no job, Eddie now can't pay off his deubters or get $$$ for his daughter. His deubters, to send him a message, burn down his house, with his daughter inside. Eddie loses it, and is going to end his life, but finds the symbiote in a church.
That, with the expanded Harry subplot, and beefing up the symbiote, would have been more than enough to keep the audience interested.