When I went into the build steps for the various build configurations, I realized I can reference the properties of dependent build configurations.
For the example above, I have the following configurations and ids:
Build, Test, Package - btp1
Deploy to CI - dtc1
Deploy to QA - dtq1
In my Build, Test Package
build configuration I configured my OctoPack
version number as:
%MajorVersion%.%MinorVersion%.%build.vcs.number%.%build.number%
Then in the Deploy configurations, I changed the version number to be:
Deploy to CI - %MajorVersion%.%MinorVersion%.%dep.btp1.build.vcs.number%.%dep.btp1.build.number%
Deploy to QA - %MajorVersion%.%MinorVersion%.%dep.btp1.build.vcs.number%.%dep.btp1.build.number%
By doing so, I was able to reference the build number of the previous builds to promote the correct release from one environment to another.