Setting up the different shipping sites as sub-customers of the parent will work here - I am in the same boat with various sites.  I always bill the parent company, with the remote site as the shipping location - my only issue is that the parent company name is always shown on the top of the shipping address, even when I don't want it to be.

Create your parent customer 

Then create another new customer, but immediately tick the 'is sub-customer' box and choose the parent company.  Then you can add in all the other information with new delivery address etc.

It is a very awkward work-around considering it was so simple on the desktop version, but once the sites are set up it becomes slightly easier.