Absolute paths workaround in web application

Question

I'm a bit of a beginner when it comes to setting up ISS and rewriting rules, so I thought I'd ask for help here. 
 
In an early stage of the project we decided to keep all urls and paths within our project absolute. Probably stupid, but we had heard that we would always be able to deploy our website to the root folder of the IIS, so this simply wouldn't be a problem in either test environments or in production. 
 
Anyhow, the business now require that we deploy the website to a new test environment. En environment that is to be shared with other projects, so we have to make a subfolder in the IIS root. Making DNS changes is not an alternative, so our website can only be reached using the url:
[serverName]/[OurProjectName]/ 
 
And obviously, no links, images etc work in this new environment. It's going to be a huge effort rewriting all paths and urls in the project. So I was wondering, is there any way to solve this problem just changing the configurations in the IIS or in the webconfig? Maybe add some rewrite rule that inserts the application folder name to each request? 
 
Many thanks!