First of all, your project sounds cool!
Aside from my current RPG map tutorials guide project, I also publish the Kaidan setting of Japanese horror (PFRPG) as an imprint under Rite Publishing with products since 2010, 3 modules, 3 one-shots, 2 racial guides, 2 class/faction guides, a haunts guide, and a haunted bath house mapped adventure location (kind of a one-shot in itself) - I'm the author of the latter product. I do game development, some game design (several freelancers involved), some illustration, all the maps, cover design and page layout. Although Steven D. Russell of Rite Publishing does all the actual marketing and administative tasks - I keep a close eye, I come from a position of experience.
So... though you may have already done some or all of this (I don't know), here's how I'd promote it.
RPGkickstarters.tumblr.comENWorld - Kickstarters forum
rpg.net - Ads/Promotion forum
rpggeek.com - Press release forum
RPGsite - News and adverts forum
Once you get posted there, then many other RPG related sites with Kickstarter List threads, add it to their list, so with only posting to those sites above, you'll be posted in dozens more automatically.
If you can afford to spend around 10% of your funding achieved,
Gamerati is the RPG industry PR company, they can get banners and bloggers in huge numbers in a very large network.
Visit
Destination RPG blog, join, send an Email to Rob asking to promote your project with an Email interview (he sends you 7 or so questions about you and your project, you answer, and it will get posted within the week (usually) as an interview blog post. He did an interview of me and my project, last week.
Visit Enworld forums, RPG net forums - look for threads about zombies and post, you can place your Kickstarter as a link in your signature block on each post. You can stay true to the thread talk about your zombie knowledge as it applies to mimize spamming your project everywhere. If asked, mention your Kickstarter, otherwise let the signature do it's job.
It's too late to start a social networking campaign (at 5 days into the project), if it were 4 months before the project, you could start a blog, G+ community, Facebook account just for your game (not a personal account), acquire an audience of 'Friends' - visiting other communities and Like or + posts and threads, being active in those communities. So when your Kickstarter begins you've already built a buzz of interest to start funding you as you begin - that's what I did, and I'm 15 days in half-way through funding, have met goal, and less than $1200 to first stretch goal.
Once you release your product make sure you contact the various RPG product reviewers
Endzeitgeist being a big one, send a free download through DrivethruRPG/RPGNow to them so a proper review can be posted at that major RPG selling site, as well as dozens of other major blogs. Hope for the best ratings, but as long as it's not 1 or 2 star, you should get plenty of airplay of your product release.
There are many reputable RPG product reviewers, find them, give them free PDFs and your exposure is increased multi-fold, especially for 4 and 5 star rated products.
There's a lot more, but that should be a good starting place for RPG marketing.