Decided that the actual backpack part would be easy - a regular hikers water carrier will be the 'case' of choice:

It already has a pocket which will be about the right size and will hold the unit close to the wearer's back.

I also have a redundant PC speaker set with subwoofer which will form the basic electronics.

Still need to arrange a suitable battery for this.

I plan to  test with the original speaker (although it's only a cheapie) as a POC. Researching around the Dayton Audio Bass Exciter looks like it will operate down the the frequency range required (sub 50Hz), so I will source one of these eventually.