Thanks OgAus!
I guess it all comes down to the type of contactor one bought/uses. Mine (Gigavac GV141PAX) is an external PWM-type (P) and draws over 2,5A current without PWM. From what I learned, by using PWM, it could be maintained with only 0,2A.
Meanwhile I ordered a DRV103 chip that does this job. Yesterday I tested a simple inline RC solution that already dropped the current to 0,8A.
Will let know the results once I found a working solution.