In the expression “your bodies a living sacrifice,” there is a plural: “bodies”, and a singular: “a living sacrifice”. This language usage sometimes implies a group doing a singular action together. This could certainly be the usage Paul intended in this verse. Such language would fit what I know of committed Christians, and also seems to be the common case in the New Testament. Christian history is filled with accounts of Christians sacrificially serving Christ together as one entity.
This interpretation rests well with the context. Previous chapters presented believers as a multiracial family of adopted children. The following verses, 3-8, illuminate this collective sacrifice by the illustrative use of a functioning human body.
“Our reasonable service” then, is not an independent venture. This service is given by an ordered group of followers which Jesus called His church. Each follower of Christ has personal gifts which are intended for use in a “body,” and are of little value alone. Make sure you are part of team of committed servants of Christ. Long-term group sacrifice creates a bond that is rare in this world. If you are looking for a church to serve in, feel free to write, and I'll try to help.
It has been my privilege in Christian service to work with committed, faithful men and women who are ready and willing to sacrifice themselves for the Savior as an effective, mobile group. To my family, our church staff, and our wonderful church family: I am privileged to serve with you. I am constantly strengthened by the knowledge of your sacrifice and love for our Savior.