@Cory Anderson‚ I just ran into this and found a work around/solution.
Although as @William English‚ mentioned, using this method would only work for your typeahead field if it is used exclusively on Programs.
On a program form, create a calculated custom field to capture the program ID (AKA: ID). I called the field Program ID (very original, I know).
Then I would apply the following text mode to the typeahead field you used called "Master Project" (which is also on a program custom form).
I wanted to try something similar. When in a project, have a dashboard pinned to the left side navbar that lists all other projects in the same program in one report and all in the same portfolio in another.
There is no way to reference the program or portfolio the currently viewed project is in though.
I suppose I could create a calc field in the project form though. Get the current project's program, then list all projects with the same program (if that's even do-able). Not as pretty as a report, and not clickable but better than nothing.
On second thought, currently, we can click on the breadcrumb at the top to see other projects, that may be good enough.