Morning Ed,
Many a good tune is being played on an old fiddle so your camera seems up to the task, a comment about double or more flashing the idea of the preflash is to narrow down the black part of the eye to reduce the reflectivity in the back of the eye causing red eye pics, I doubt your pens will suffer from this.
Just a week or so ago I bought a sheet of WHITE Cardboard after years and years of using copy paper 11 by 14 inches cause dammit it gives a slight caste, from what I can see of your cake box it will have fillers etc to repel cream etc and also may give you a caste in your pics. One such filler commonly used in paper products is the colour blue to trick the eye into creating a stronger white remember Reckits Blue Bags that did just that.
Flimsy is never a way to repeatability all photographers me included after well over 60 yrs of being one and qualified at that since the 60,s aim for what we call an endless background this means simply a means of creating a back curve from the flat anyway please go back over my contributions and look carefully at my open light box that for me has all the boxes ticked not just one cake box.
Ed I think from memory we had this conversation before and I wish you well in whatever you do. The answer my friend is keep it simple, sturdy enough to stand up to the years and strong enough to support overhead lighting etc.
Kind regards Peter.