While the characteristics of the trumpet (or other brass instruments) will cover any inconsistencies in your double-tonguing technique, the recorder will not. You'll need to very carefully work on evening out the syllables. Simply thinking of an even, uninterrupted airflow will help, but you'll likely need some additional work. Visualize a continuous airstream throughout the double-toungued phrase, and your articulations as simply placing dents in the airstream. Or visualize your tongue as floating on the airflow. That in particular helps me.
Finally, to even out the syllables, try single-tonguing using the syllable (ka or ga) that you use for the second syllable of your double-tonguing technique. Then double-tongue, but reverse the syllables. I imagine it'll take a lot of work to even out enough to sound consistently great on a recorder.
EDIT for your edit: I would try using the syllables "da-ga" or "doo-goo." In my experience, they are softer, and more naturally even syllables. They may work better on the recorder. I would tongue that circled measure as: "da-ga-da-ga da da." This is easy on brass, more difficult to get even on recorder. If you still have the problems with overblowing the second syllable even with the "da-ga," try using the backwards technique I detailed above; it really helps to make them even!