To work around the issue, I created a materialized view that I can update periodically, and of course I can query said view in no time flat. However, I’m concerned that as the dataset grows, the time it takes to refresh the view will also grow (correct me if I am wrong there).
I'd probably turn that index into a foreign key that just ensures that every (station,channel) that appears in the data table also appears on the lookup table. Grouping and array-ifying the lookup table would be trivial. Either modify the application code or add a trigger to populate the lookup table as needed.
The parentheses around channel in "array_agg(distinct(channel))" are unnecessary - you are invoking composite-type syntax, which is ignored in the single column case unless you write the optional ROW keyword, i.e., distinct ROW(channel)