Recurring Memberships
I don't have any idea about eWayrecurring extension 

we did something similar and our base extension was https://civicrm.org/blog/andyw/offline-recurring-payment-extension

offline-recurring-payment-extension - this extension was creating contribution for a contact which we altered to link with membership

The process which you have explained will create multiple contribution for a single membership

Other way of doing the same would be 

Using partial membership which will allow multiple payment for a single contribution - that involves bit more development - still to come in core 

I guess this helps !!!