Is there a way to do this without giving them "edit all" permission on the Account object:
2 answers
From your description, it sounds like your meetings (events?) have a Controlled by Parent sharing model, forcing users to have account edit access in order to edit the meeting record. Please correct me if any of that is wrong.
You can grant your SDRs access to edit accounts by creating a Sharing Rule under Sharing Settings in setup. You could potentially use the role hierarchy to grant SDRs access to any account, or only those belonging to specific roles or divisions in the business.