There is a way to do that which is sort of custom - and a little bit of work.
Because you have many sections already you don't want to use the 'section' option for media source on your main page - it just won't work.
But, you can create exhibits in the main section and do the following:
- create Exhibit Links (in the main section)
- title with the name of your project you want to link to
- input the correct url to the corresponding exhibit
- upload one corresponding image for the project
- hide them from index via Page Options
Now, if you have the main page media source set to 'section' it will show all of these exhibits with links to the projects. This way, you can customize which projects appear on the main page in whatever order you wish.
Does that make sense?