Hi I just saw your question now..I always book direct either with holiday rentals or owners direct when we go to Fuerteventura...
not sure which area you plan to stay in but if it's correlajo I can give you the contact details of an Irish owner..we stayed there in Jan.a 1 bed apartment in lovely complex walking distance to town..
In Caleta we stayed on the golf course again using an Irish owner..a lovely 2 bed semi detached house ..this is a 20 min walk to town and a €3 taxi home...PM me if you want details