I do a lot of media buying in this area, and there are a bunch of different options that would cover what you're looking for. Off the top of my head, ZipRecruiter.com essentially acts as a centralized hub to push your job ads elsewhere. I'm not sure if they work with Dice, but I know that from ZipRecruiter you can push jobs to Craigslist, Monster, Careerbuilder, LinkedIn, Twitter, etc. Their pricing structure is sort of all over the place, so I'm not sure if it fits what you're looking for or not, but that's not a bad place to start.
Additionally, Bullhorn Reach is a completely free service that links your ads to LinkedIn, Facebook, Twitter, and a couple of other social networks. It's easy to use, and free, but social recruiting isn't all that useful frankly, unless you have a really specific sort of connections on LinkedIn/follower base on Twitter. Bullhorn Reach will save you time though.
I'm not 100% clear on what your company does, but I know it's IT related, so Github might be a solid niche option for you, and I've even had some success posting on local subreddits in the past.
You might also want to look into sponsoring some campaigns on Indeed. They're far and away the biggest driver of traffic in the industry, so if you have consistent needs, putting the money you'd have spent otherwise on Dice towards PPC campaigns there would likely be more fruitful.
I do a lot of consulting on this for companies of all sizes, so if you have any other questions feel free to ask.
Edit: I should also add that the LinkedIn job board itself is a better option than Dice. My experience with Dice has always been that the ads don't generate a ton of response, though there's a reasonably high resume quality, and that the resume database there tends to have a lot of candidates who need sponsorship.
