It looks like there is no way to do this, so I may just end up writing a console app.

I need to call an REST service via HTTP, and take the output from that and use it to set a custom header in another REST service HTTP call.

It would be really cool if the HTTP task had output functionality (Web Service tasks have this, but nothing else?) and also if you could set arbitrary headers on the HTTP task.

Well, I guess I found my own solution. The simplest method seems to be to just use a Powershell task and call Invoke-RestMethod and pass the content to a second Invoke-RestMethod call.