Taking individual subjects not related to my career
As a faculty member of a German university that also offers a Biomedical Engineering program I can confirm that the admission rules can be quite strict.
However, in almost every study regulation is a clause that the program's examination board (Prüfungsausschuss) can overrule any formal requirement.
The keyword here is "equivalence". E.g., being a software developer can compensate missing software classes, etc. Additional certificates from courses at your home university (as you suggest), even if you take them outside a regular program, can help as well.

So my advice is to bypass the administration and contact directly the head of the program's examination board, or (if such person exists at your target university) the head of the study program (Studiengangsverantwortlicher, sometimes, s/he is the same as the study dean of the program, but not always) and ask what would be needed to prove equivalence.