There is a pseudo water bottle that somebody has on the market that you can store your stuff in; or there is a hot drink coffee mix that comes in a plastic container with screw-on top that also fits in a bottle cage that you could utilize. The Bento Box bag will fit on toptube/stem juncture. There is also a stoker handlebar bag available.
And you can use a standard rack on rear by using commercially available extender for rear rack to the 2 rackbolts on rear of Burley and (gasp!) carry a small bag on the rack.
Lots of options!