You're on the right track with link building and anchor text. It's important to sculpt your priority pages with the branded terms (on page and in the code). You're lucky to have a team working on link building as that takes effort, but well worth it.
I think it would be tough to obtain 100% dominance, but one thing you might try is adwords with your branded terms. In this way, you appear more on SERPs. Kind of like driving down the highway and seeing multiple billboards vs just a few. With more, searchers are more likely to click on your links. Adwords is also a great way to test branded keywords to see traffic and click data, that you can apply when creating your webpages around those terms.
One more think is anchor text linking within your site so that the architecture throughout the site has pages with branded terms linking to your important pages.