I assume sub amp and tuner are 1U each and the main amp is at least 2U. If that is the case you could use a 4U "Desktop Rack" and have it sit on its side. If you need more than 4U i dont think you will find anything that will fit.

I would leave enough cable so that you could lift the rack in and out of the cabinet and put it on the floor for service. Put tech flex around the cable bundle.

This one is 9" x 20.75" x 16" :

[Link: sweetwater.com]

This one is 8.25" x 20.25" x 16" :

[Link: sweetwater.com]

You may be able to find a 5U or 6U case like this with thinner sides making the overall depth smaller. Everything i found goes like this 2U/4U/8U/16U so nothing at 5 or 6. Maybe you could have a flat steel frame welded with rack rails to make a custom rack for this project.