Journalist with Three Hour Deadline

I’ve been on a trial assignment for the past week where I submit a story three hours of receiving the assignment — it must have quotes from two original resources (not PRs, research reports, and so on). I understand that because it enhances a story and makes it more interesting.
Not once have I turned in an article on time. I called and emailed the right people — I know I didn’t err there. You know there’s one thing I do differently — I use the relay service to make the calls because I can’t hear a phone conversation. Here is what happened on one assignment alone:

• Called a research firm. Before I even get to type… hung up.

  
  Called back same firm with a short message for the relay operator to give to the guy before he speaks. “She’s already contacted us.” hung up
  It was true I had contacted someone else by email — but not him. I don’t limit myself to one press contact because you never know how busy the person is or if they’re even in. Often, I’ll let them know who else I’ve contacted within the company.

• Called a research analyst directly — proud of the research I did to find him. I started off the conversation introducing myself, the publication, and that I had sent an email to interview him.
  “I see the email.” hung up. Never heard from him.
• I reached the company that issued a report on which I was writing the article. The researcher who did the report was not available to the press. “Then why did you issue a PR if you don’t want us talking to you? Oh, you want us to promote your report. Well, I want an original quote not something everyone else quoted from your PR.”
  By the way, the report had two other names listed — I asked to talk to them. No. The guy is the main one to talk to and I can’t talk to him.

And I’m trying my darndest to do a good job just like anyone else. I asked the editor if anyone else had the same problem I had. He said I was the only one struggling. I’d be the first to admit a mistake, but I can’t see where I’m going wrong and the only difference between other reporters and me… the relay.
Okay, there may be one more difference. I don’t have established contacts with some of these businesses. But I am sure I’m not the first one they’ve tried out.