I have used CommunityCommons.executeMicroflowInBackground to run various background processes and conversions. It does allow you to pass one object. Only one microflow is allowed to run at a time.
Create a non-persistent entity to and put all the data and headers in that you need to pass. Specify your microflow that will call the REST service and your object on the call to executeMicroflowInBackground.
In the microflow, setup your REST call with headers and make the call.