Re your 'pest issue' - have you established that the rodents are definitely getting in via the doors?
Unless you can completely rodent-proof your doors, rats or mice will gnaw through brush strip or rubber bumpers to gain entry if they are accustomed to getting into your building that way.
Yes, you need to eliminate the gaps but you also need to address the existing rodent infestation outside as well as inside.
Where are your rodents coming from; is there vegetation or stored materials near your loading doors that are providing cover to allow them to approach the building?
Make the exterior as non rodent-friendly as possible and carry out treatment against the external population prior to installing your new proofing - otherwise the existing rodent population will attack your new brush strip!