(Not a Teacher)
Here's my take on that sentence:
"My adaptability to new environments, people, and equipment ensures that I will be able to seamlessly integrate with your team while maintaining its international mobility."
For the second sentence...well, this may be a somewhat dramatic, but tell me what you think:
"My values are more than inseparable from my career objectives; they are enshrined within them."
When I hear 'preponderant', the first meanings to come to mind are 'overbearing' or 'overwhelming'. While the word also has the meanings 'prevalent' and 'important', which you were utilizing for your original sentence, I feel the somewhat negative connotations of the word don't fit with the statement you're trying to make about your values.
Student or Learner