Contact a local car rental company instead of international companies. Talk to them and ask how the can handle such a case. I am pretty sure local companies in Iceland are more able and willing to handling such a case.

With the big car rental companies, local agents often have restricted responsibilities and possibilities for handling more complex cases. I made my experiences...

Or book your car via a travel agency, then you may not need at credit card at all.

Contact a local car rental company instead of international companies. Talk to them and ask how they can handle such a case. I am pretty sure local companies in Iceland are more able and willing to handling such a case.

With the big car rental companies, local agents often have restricted responsibilities and possibilities for handling more complex cases. I made my experiences...

Or book your car via a travel agency, then you may not need a credit card at all.