Take a look at the guidelines for WCAG 2.0 compliance: https://www.w3.org/WAI/WCAG20/quickref/
Level A compliance should be achievable, even with the limitations your organization has placed on you. It may require a bit of additional hours, but shouldn't significantly increase the scope or cost of a project. Things like, provide text labels for important visual elements like icons in navigation. Enable users to navigate page elements and forms using their keyboard (without a mouse). Test to make sure your products can be read by screen readers.
Most organizations I've been a part of shoot for Level AA compliance.
Here's a quick summary of the differences between Levels A, AA, and AA:
Level A Success Criteria are those which will have a high impact on a broad array of user populations. In other words, they (usually) don’t focus on one type of disability only. They will also have the lowest impact on the presentation logic and business logic of the site. Finally, implementation of these requirements will typically be the easiest.
Level AA Success Criteria will also have a high impact for users. Sometimes only specific user populations will be impacted, but the impact is important. Adherence to these Success Criteria may impose changes to a system’s presentation logic or business logic.
Level AAA Success Criteria are often focused on improvements for specific user populations. They may be difficult or expensive to adhere to, depending on platform limitations. The benefit-to-cost ratio may be low enough to de-prioritize these items.