What are the most cost effective “go-to” brand exercises for creating a consistent and compelling brand story across activations?

It is important to develop a brand guide, brand resources and training to back up the brand story. Very often you'll find that as you get further out from C-level management, the adherence to the brand story goes away. Put another way, sales will develop their own story or stories. You must provide a cohesive story and the training and materials to back it up. Part of this is line of management buy-in to the brand story and how to handle sharing it with their teams and ensuring every one is trained to use it. 

Creating a consistent brand story across all marketing activations stems from building a unique brand identity, in the first place.
Many marketers skip this fundamental and preliminary step, in a hurry to set up campaigns, attract traffic and conquer share of voice, falling into some sort of operational rush.
Crafting a unique brand identity requires time, planning and research: it is a matter of nailing down that irreplaceable differentiator, that makes that brand stand out from competition at all times.
Creating a story around it will then naturally follow, if the identity definition is clear and competitive. 
Think of your brand identity as a character of a drama series and the brand story-telling as a set of staged scenario's where that character will perform its role, truthful to its personality.

1- Here's some recommended steps to create a consistent brand-story telling:
Create a gap analysis of your brand identity against your top competitors (remember: each channel is a different battle field with different competitors). Identify your competitive and unique brand connotation both within each channel and across all;
2- Once you find that, "put on stage" that feature in different scenario's and create a story around it in a way that sounds personal, resonates with your audience at a lifestyle and mindset level. Neuromarketing will be a great aid in that regard. Use it;
3- Show the "character" (your brand identity) from different angles, like through a prism, but treat it as a person, therefore with consistent personality traits; even the most authoritative and institutional brand must sound personal and speak to end-users, real people;
4- Set clear KPI's for your activations strategies that measure the level of engagement of the intended audience with your brand-story settings.
5- Analyze aspects in your story telling where your brand connotation is weak or uncertain and find ways to enhance your brand identifiers. Relevant semantics, interactive experiences, brand affiliations and co-marketing strategies, sponsorships of events: all of this can contribute to reinforcing your brand identity consistency and offer new story-telling opportunities;
6- Do not lie on your brand. Do not position values, promises and pluses that you cannot really offer with the product that stands behind your brand. Authenticity is the first key to consistency.

First, audit what you're doing for consistency. Then, implement a content strategy. Gartner has significant resources on creating and executing upon content strategies.