It seems like you believe that in this situation, the best answer would be quality over quantity. This is surprisingly not true. Often times in music the goal of a trill is to add an additional bit of flare, excitement, or to overall complement the piece. The trill is supposed to be fast in order to be effective. Now if you do a regular C to D trill, the fact that you have a lower quantity utterly destroys the quality of this section.
Seemingly, it is always best to go with an alternate fingering when it comes to tricky trills. Because trills are meant to be fast, they are not judged on the quality of the tone like other notes. Rather, they are judged on how they are able to complement the rest of the music. Making sure that your trill has a correct consistency in order to make it “efficient” is key. Using regular fingerings (at least for flute) in this case will not be able to compare to the use of an alternate.
If you are would like some ways to increase your agility outside of trills, there are many ways you can do so. Being able to switch fingerings at a faster rate is always something you can work on, and is applicable in so many separate ways in music. You can easily find these online just by searching scale exercises, agility exercises, tonguing exercises, etc. A surprisingly easy thing is simply by going up and down a regular scale. A method you can use is what I call “the jump method”. You start by playing your first note, then you play your first and second notes, then your first, second and third notes, etc and then you go back down. Another way is by jumping up in thirds, or playing sixteenth notes to uncomfortable fingerings (side note, but when there are quickly played uncomfortable fingerings, you can also use trill alternates if needed). There are all kinds of ways you can increase your agility, but if you need a place to start simply look to scales.
I hope this was able to help!