You are going to deliver news to your readers via the internet. You break it on the web, you break it as soon as you have it, and you develop it online. And then, and only then, do you analyse, contextualise and develop it on paper. And you hope and pray that you’ve done a good enough job developing it on the web that your readers will trust you enough, and value your judgement enough, to shell out for a paper product to enjoy at their leisure. Paper is a vehicle for analysis, for depth, for a sit-back-and-think experience. The internet is for news.
Your recalcitrant reporters are going to have to ask themselves this question: what’s more important to you: breaking stories or making a paper widget? If their instinct is serving readers, then they’ll find the time to go web first. If their instinct is generating a print product, you might want to point them in the direction of a career change advisor. 
Journalism is a process, not a result. We find stuff out, and we get it to people in as timely a fashion as possible. And the internet is the most efficient news delivery device we have. If you’re not interested in delivering news to your readers quickly, you’re not a journalist, you’re just pretending to be one so you can feel good about yourself.
Say it with me again: paper doesn’t deliver news; the internet does