Thank you very much for the advice!
I solved the problem, partly by doing what you described in your post. Here a description as it might possibly help someone else:
The problem lies in the nature of the surface depicted in the images. As it is a glacial area there are many areas that are snow covered. So as there basically is no distinctive structure in large areas it seems hard for the matching algorithm to automatically find a sufficient number of tie points.
A further problem I identified was that the structure that IS visible (like glacial mills and single rocks) are of such generalized structure that they match in other images that do not cover the particular geolocation of the uncalibrated images. So for most of the images the problem was that a higher number of false matches were found than actual true matches.
What I now did was I processed the single strips that contained the uncalibrated images (as those were spread all over the whole area of interest) and thus decreasing the number of possible false matched patterns. In a single case I had to use manual tie points. By iteratively adapting the camera parameters I was finally able to calibrate the failed images in the single strips. I then merged the strips one after another with the whole block.
This lead to only 3 images left that I am not able to calibrate. This is (from my guess) because they consist of mostly snow covered areas. As they are in the border region of the block and do not contain information I need (as they are not part of the overall area of interest) I can live with them not being calibrated.
Thank you again for your help!